Lenk, J.
After trial by jury, the defendant, Patricia Cheromcka, was convicted of two counts of larceny over $250 and one count of larceny under $250. G. L. c. 266, § 30. She was acquitted of conspiracy to commit larceny in violation of G. L. c. 274, § 7. The charges stemmed from Cheromcka’s alleged misuse of school funds in the period between April 1, 1996, and May 31, 2000, when she was the business manager and director of transportation for the Southeastern Regional Vocational-Technical School District (district). As business manager, Cheromcka was responsible for the day-to-day operations of the district’s business office; her duties included, among other things, obtaining supplies and equipment, approving purchase orders and bills, and maintaining a petty cash fund. In her capacity as director of transportation, she supervised the district bus drivers and their direct supervisor, Barbara Ataman.
The grand jury returned three larceny indictments. As reflected in the bill of particulars, the first alleged that Cheromcka committed larceny by falsifying bus drivers’ time sheets to reimburse the drivers for running her personal errands. The second indictment alleged that she stole cash from the sale of soda at the school bus depot. The third indictment was in three parts alleging that she (a) used her school district credit card [773]*773for personal expenditures; (b) misappropriated district travel funds; and (c) submitted falsified vouchers to replenish the petty cash fund from which Cheromcka pocketed cash.
On appeal, Cheromcka claims error in two respects. First, she maintains that the evidence was insufficient to support guilty findings on the three charges of larceny. Second, she contends that certain opinion testimony was admitted in error and created a substantial risk of a miscarriage of justice.
I. Sufficiency of the evidence. General Laws c. 266, § 30, inserted by St. 1945, c. 282, § 2, provides, in pertinent part: “Whoever steals, or with intent to defraud obtains by a false pretence, or whoever unlawfully, and with intent to steal or embezzle, converts, or secretes with intent to convert, the property of another as defined in this section, whether such property is or is not in his possession at the time of such conversion or secreting, shall be guilty of larceny . . . .” Section 30 merged into one crime, larceny, what had formerly been three separate crimes: larceny by stealing, embezzlement, and larceny by false pretenses. Commonwealth v. Mills, 436 Mass. 387, 391-392 (2002). Larceny can be established by evidence warranting a conviction on any of the three theories. Ibid. See Commonwealth v. Williams, 63 Mass. App. Ct. 615, 620 n.7 (2005).
The first and third indictments were submitted to the jury on a theory of false pretenses, while the second went on a theory of larceny by stealing. Although claiming that the evidence was insufficient to support any of the indictments, Cheromcka takes particular aim at the first and third indictments for having gone to the jury on the wrong theory of larceny. The thrust of the Commonwealth’s case on these indictments, she claims, is that Cheromcka was legally responsible for district funds which she misappropriated for her own use. This is classic embezzlement, but embezzlement was not the theory on which the first and third indictments went to the jury. They went instead on false pretenses, as to which the evidence, she argues, was simply insufficient to sustain the convictions. Commonwealth v. Mills, supra at 397-399.
As a threshold matter, we dispose of Cheromcka’s argument that, because the Commonwealth’s theory before and during [774]*774trial was impliedly embezzlement, it cannot on appeal rely on a theory of larceny by false pretenses. All that need occur is that the evidence adduced at trial be sufficient to prove the elements of any of the three theories of larceny and that the jury be instructed on the theory of larceny as to which sufficient evidence was adduced at trial. Id. at 392. That happened here. The Commonwealth is not required to “elect its theory of the manner in which the . . . larcenies were committed. . . . ‘Where a crime can be committed in any of several ways, . . . the defendant should be convicted if it is proved that he committed the crime in any of those ways.’ ” Id. at 392-393, quoting from Commonwealth v. Liberty, 27 Mass. App. Ct. 1, 9 (1989).1 Neither the indictment nor bill of particulars need articulate a particular theory of larceny. See Commonwealth v. Mills, supra at 393. See also Commonwealth v. Nadal-Ginard, 42 Mass. App. Ct. 1, 5 (1997). It is sufficient that the jury be instructed as to a particular theory of larceny, as a “criminal conviction cannot be affirmed on appeal where the jury were not instructed on the elements of the theory of the crime.” Commonwealth v. Mills, supra at 398. Here, the Commonwealth did not elect a theory of larceny as to any of the indictments until the end of trial, just prior to jury instructions. At that point, it elected larceny by false pretenses as to the first and third indict-[775]*775merits and larceny by stealing as to the second. The judge’s instructions as to each, including larceny by false pretenses, were “full, fair and clear as to the issues to be decided by the jury, the rules to be followed . . . , and the law they [were] to apply.” Id., quoting from Pfeiffer v. Salas, 360 Mass. 93, 100 (1971). Hence, the jury had before them the applicable elements of the crime.2,3
[776]*776Standard of review. We review the sufficiency of the evidence to determine “whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt” (emphasis in original). Commonwealth v. Latimore, 378 Mass. 671, 677 (1979), quoting from Jackson v. Virginia, 443 U.S. 307, 318-319 (1979). See Commonwealth v. Arroyo, 442 Mass. 135, 139-140 (2004) (“we must determine whether the evidence presented at trial, together with all reasonable and possible inferences that might properly be drawn from it, was sufficient to permit a rational jury to find beyond a reasonable doubt the existence of every essential element of the crimes charged”).
Indictment one. Larceny by false pretenses: falsifying bus drivers’ time sheets. “(Pjrosecution for larceny by false pretenses requires proof that (1) a false statement of fact was made; (2) the defendant knew or believed that the statement was false when he made it; (3) the defendant intended that the person to whom he made the false statement would rely on it; and (4) the person to whom the false statement was made did rely on it and, consequently, parted with property.” Commonwealth v. Williams, 63 Mass. App. Ct. at 620, quoting from Commonwealth v. Mills, supra at 396-397. The gravamen of the crime is that the victim’s reliance on the swindler’s misrepresentation causes the victim to part with his property. See Commonwealth v. Williams, supra at 621-622.
The district had a fleet of buses used not only to pick up and deliver children, but also for field trips and sporting events, runs to the bank, and other school-related business; for most trips drivers were paid an automatic minimum.4 Three drivers testified that they frequently ran personal errands for Cheromcka,5 for which extra hours were added to their time sheets; the [777]*777additional compensation was reflected in their district paychecks.6 Thus even if a driver ran a personal errand for Cheromcka within the automatic pay period, there were times when Cheromcka added extra hours to the time sheet above and beyond that automatic minimum.7 Cheromcka claims that the Commonwealth failed to prove larceny by false pretenses since (1) her initials on the bus drivers’ time sheets did not constitute false representations; (2) there is no evidence that the district relied on her initials; and (3) she did not obtain any property.
Cheromcka’s first two contentions need not detain us. The addition of extra hours on the time sheets constituted “a bill for labor [which] may be found to be an implied representation that the charges are correct,” Commonwealth v. Louis Constr. Co., 343 Mass. 600, 604 (1962), and “could reasonably have been found to have set in motion a course of procedures by which the misrepresentations of the invoices (through an unbroken chain of causation) eventually influenced” the district. Commonwealth v. Leonard, 352 Mass. 636, 645 (1967).
The matter is more nuanced as to Cheromcka’s third contention, i.e., that her conviction cannot stand because she did not obtain “property” within the meaning of the common law or G. L. c. 266, § 30.8 That the school district parted with property in the form of money is not at issue; it paid the drivers for the [778]*778extra hours that Cheromcka added to their time sheets. Cheromcka, however, directs our attention to the question whether larceny by false pretenses may lie when what she obtained — services — is not itself property.
Ordinarily, of course, the very property with which the victim has been induced to part is what ends up in the hands of the swindler. See, e.g., Commonwealth v. Mills, supra at 397; Commonwealth v. Nadal-Ginard, 42 Mass. App. Ct. at 8; Commonwealth v. Lepper, 60 Mass. App. Ct. 36, 42 (2003). Nonetheless, larceny by false pretenses may “encompass[] more than direct dealings between the defendant and the defrauded party.” Commonwealth v. Williams, 63 Mass. App. Ct. at 622. See Commonwealth v. Mycock, 315 Mass. 262, 266-267 (1943); Commonwealth v. Hamblen, 352 Mass. 438, 443 (1967).9
Cheromcka relies on Commonwealth v. Rivers, 31 Mass. App. Ct. 669 (1991), and Commonwealth v. Geane, 51 Mass. App. Ct. 149 (2001), for the proposition that fraudulent inducement of services is not larceny. Neither case is controlling here. In Rivers, we held that larceny did not lie where a contractor used a town landfill for dumping without paying the town the requisite fee. Such unauthorized use, we concluded, is not “property” that may be the subject of larceny. Commonwealth v. Rivers, supra at 670-671. In Geane, we held that a contractor who induced subcontractors to provide construction services on the false promise of later payment could not be liable for larceny because such services are not “property” within G. L. c. 266, § 30, or the common law. Commonwealth v. Geane, supra at 154. In each case, the victim — the town and the subcontractors, respectively — did not part with any “property” that could be the subject of larceny. That is unlike the case now before us where the district did part with property — it paid the bus drivers money for services rendered not to the district but to Cher[779]*779omcka, for which services she herself would otherwise have had to pay. Not to put too fine a point on it: what Cheromcka stole, albeit indirectly, was the district’s money. The evidence before the jury that she knowingly falsified the bus drivers’ time sheets and that the district, relying on those falsifications, parted with property in the form of money sufficed to support her conviction of larceny by false pretenses.
Indictment three (a). Larceny by false pretenses: credit card use. The purchase of supplies and materials for the district was subject to a multistep approval process10; this approval process was not required, however, for purchases made using the school’s credit cards. All bills for school-related purchases, whether made through the purchase order process or by use of credit cards, came directly to Cheromcka. It was part of Cheromcka’s job as business manager to approve such bills before forwarding them to the accounts payable clerk, her subordinate, for submission to the school committee as part of a warrant requiring committee approval.
Cheromcka was authorized to use two district credit cards, one issued by American Express and another by MasterCard; Cheromcka testified that both were issued to the Southeastern Regional School District, but it is unclear whether both names, the district’s and Cheromcka’s, were on the cards.11 After James Hager became the district superintendent in September, 1998, he reviewed the district’s credit card bills and noticed that while the bills from the credit cards issued to Cheromcka had been paid, there were no corresponding receipts for the items charged. [780]*780Cheromcka agreed to provide the receipts, but when Hager later reviewed what Cheromcka had provided, he noticed that some receipts did not describe the purchases, some were “rather strange,”12 and others were for purchases made in New Hampshire.13 He could not account for at least one purchase — a Christmas tree that Cheromcka claimed she had purchased for the school’s restaurant, the Colonial Room; Hager testified that, in response to his inquiries, he found no employee who had seen the tree. In addition, there was testimony that Cheromcka paid for a birthday dinner for Ataman and friends with the district card.14
The Commonwealth contends that, by signing the credit card slips, Cheromcka falsely represented to the district that the charges were for legitimate school expenditures. This is unpersuasive. Cheromcka’s signature only represents the cardholder’s intention to repay the issuer.15 See Citibank (S.D.), N.A. v. Hansbury, 128 B.R. 320, 321 (Bankr. D. Mass. 1991). See also MBNA America Bank, N.A. v. Ashland, 307 B.R. 317, 322 (Bankr. D. Mass. 2004) (credit card transaction is contract wherein cardholder promises to reimburse card issuer for purchases charged). Since the district did pay the issuer, Cheromcka’s signature cannot be considered a misrepresentation, let alone a misrepresentation made to the district.
The Commonwealth also asserts that use of the credit cards for personal purchases is outside the scope of authority granted Cheromcka by the district. There is nothing in the record, [781]*781however, to indicate that Cheromcka made any representation to the district that she would use the credit card solely for school-related purchases. While this is perhaps a permissible inference, so too would be the inference that Cheromcka could use the card for personal expenditures as long as she subsequently reimbursed the district.
While neither Cheromcka’s signature nor her use of district credit cards to make personal purchases establishes the misrepresentation necessary to prove larceny by false pretenses, the evidence is otherwise as to her approval of the credit card bills. A false statement of fact “may be made by implication as well as by verbal declaration.” Commonwealth v. Louis Constr. Co., 343 Mass. at 604. See Commonwealth v. Reske, 43 Mass. App. Ct. 522, 525 (1997) (“false pretense may consist of an act, symbol, or token calculated to deceive”). A bill submitted that the defendant knows to be incorrect “constitutes a false presentation . . . sufficient to support a conviction of larceny by false pretenses.” Commonwealth v. Borons, 379 Mass. 117, 144 (1979). Cheromcka’s approval of credit card bills that were then submitted to the school committee for payment was an implied misrepresentation that the items purchased were intended for school use. It may be fairly inferred that, before approving the bills for payment, Cheromcka would review them and would know that some charges reflected her personal purchases.
Given this and Cheromcka’s longstanding involvement with and knowledge of the approval process, there was sufficient evidence to establish that Cheromcka had knowingly made a false statement of fact intending that the school district would rely upon it. See Commonwealth v. Iannello, 344 Mass. 723, 735-736 (1962) (intent to deceive properly found given defendant’s familiarity with submission process, falsity of bill, and knowledge of its falsity; determination of intent is to be resolved by jury in light of all attendant circumstances). See also Commonwealth v. Kiernan, 348 Mass. 29, 46-47 (1964), cert. denied sub nom. Gordon v. Massachusetts, 380 U.S. 913 (1965).
It is evident from the district’s payment of the credit card bills that it relied on Cheromcka’s misrepresentation that the [782]*782credit card bills, which she approved, reflected charges that were incurred for school-related purposes; the district consequently parted with property. See Commonwealth v. Reske, supra at 524. In so doing, the district paid for Cheromcka’s personal purchases and discharged her personal debt. See MBNA America Bank, N.A. v. Ashland, supra at 322. The evidence accordingly suffices to sustain the conviction for larceny by false pretenses as to her use of the district credit cards.
Indictment three (b). Larceny by false pretenses: misappropriation of travel money. Cheromcka was one of several district employees and school committee members who attended a conference in Florida in February, 1998. The superintendent at that time advanced all the district’s other attendees $400 for small cash expenditures; he advanced Cheromcka an additional $1,000. She testified that she took a larger advance because she was responsible for paying some of the expenses of others on the trip; there were, however, no receipts specifying what expenses accounted for the $1,400 Cheromcka received. The Commonwealth claims that Cheromcka misappropriated the money for her personal use.
A defendant who acquires the property of another by virtue of a promise, and then changes her mind and converts that property to her own use, cannot be convicted of larceny by false pretenses absent proof of an intention to deprive at the time of the representation. See Commonwealth v. True, 16 Mass. App. Ct. 709, 711 (1983); Commonwealth v. Stovall, 22 Mass. App. Ct. 737, 741 (1986). Although the jury could infer that, when she took the $1,400, Cheromcka promised to use it for school-related purposes, there is no evidence of record showing that she did not in fact do so. Even if she did use the money for personal purchases, there is no evidence that, at the time she took it, she intended to use it for nonschool purposes. A mere failure to fulfil a promise does not constitute a misrepresentation, Commonwealth v. True, supra at 711-712; absent any indication of Cheromcka’s intention to deprive the district at the time she accepted the advance, her conviction of larceny by false pretenses for misappropriating travel money cannot stand.
Indictment three (c). Larceny by false pretenses: petty cash fund. As business manager, Cheromcka was in charge of the [783]*783district’s petty cash fund, which was maintained at $300. The fund was used to pay for, or reimburse payments made for, small purchases as to which a purchase order would be too cumbersome and time-consuming. Typically, Cheromcka would total the amount removed from petty cash each month, represented by receipts, and, when the fund was depleted, fill out a voucher — a request for payment — in that amount; the voucher was then attached to the monthly warrant submitted to the school committee. Once the committee had approved the warrant, the accounts payable clerk forwarded to Cheromcka a check made out to petty cash to replenish the fund; Cheromcka thereafter endorsed the check and, it may be inferred, cashed it.
In February, 1999, Hager reviewed the petty cash fund file and found vouchers, many in excess of $1,000, for the monthly reimbursements; no receipts, however, were attached. Although Cheromcka then agreed to submit the relevant receipts, when Hager checked about two weeks later he found some vouchers without receipts, and six of the original vouchers missing. Cheromcka represented that she had put all her receipts in the file and did not know the whereabouts of the missing vouchers. A subsequently generated computer printout of the total petty cash expenditures indicated that in fiscal year 1997,16 the petty cash fund was reimbursed in the amount of $23,559.73; in 1998 it was reimbursed $32,899.58; in fiscal year 1999 the reimbursement fell to $12,807.60.17 Karen Roberts, a certified public accountant and certified fraud examiner retained by the district in May, 2000, testified that Cheromcka’s personal bank account contained approximately $55,000 which could not be accounted for by traceable deposits such as salary checks, Social Security payments, or transfers from other accounts.
Cheromcka contends that the vouchers represent promissory statements that the money to be received would be used for district purposes and as such are not misrepresentations. See Commonwealth v. True, supra at 711. The flaw in her character[784]*784ization, however, is that the vouchers functioned as a means of replenishing the petty cash fund. Hence, the vouchers were representations that district money had already been spent for school-related purposes.18
There was evidence before the jury that (1) the vouchers that Cheromcka prepared and submitted with the warrant were for the purpose of replenishing the fund which had been depleted in order to reimburse for school-related expenditures already made; (2) checks were made out to the petty cash fund in amounts corresponding to the vouchers; (3) several receipts and six vouchers were missing19; (4) the petty cash fund was designed for small purchases and capped at $300; (5) for fiscal years 1997 through 1999 the fund was reimbursed in the amount of approximately $69,000; and (6) during that same period unaccounted for deposits to Cheromcka’s personal bank account totaled $55,000. The jury could have found that Cheromcka had obtained the district’s property by misrepresenting in the vouchers the amounts that had been expended for school-related purchases. See Commonwealth v. Kiernan, 348 Mass. at 47 (jury could reasonably infer from all relevant circumstances that defendant knew and intended that victim would rely on false statement and bank would transfer money). The evidence was therefore sufficient to sustain a conviction of larceny by false pretenses as to Cheromcka’s misappropriation of the petty cash fund.20
Indictment two. Larceny by stealing: bus depot soda money. [785]*785Cans of soft drinks were kept in a refrigerator at the district’s bus depot for purchase by the twenty-six or so district bus drivers; the drivers would take a soda and put money, usually thirty to thirty-five cents, in a nearby small container. Donna Gramazio, one of the drivers, testified that she saw Ataman or Cheromcka collect the money from the container on a daily basis from 1996 to 1999 and place it in a manila envelope which she put into her pocketbook. Although the amounts collected are unclear, for the months when the cash was tallied the amounts ranged from twenty-five to forty-four dollars.
In late 1999, Gramazio took over as supervisor of transportation, regularly collected the soda money herself, and delivered it to Cathy Spurr, the accounts receivable clerk for the school from 1988 to 2000. At a February, 2000, school committee meeting, Cheromcka explained that she had collected the soda money and turned it over to Spurr or Gramazio; Spurr testified that she never received the cash during Cheromcka’s tenure as director of transportation, first receiving it when Gramazio took over that portion of Cheromcka’s duties in late 1999.
Cheromcka argues that there was insufficient evidence to convict her of larceny by stealing the bus depot soda money. To constitute larceny by stealing, there must be evidence of an unlawful stealing of the personal property of another with the intent to deprive that person permanently. Commonwealth v. Christian, 430 Mass. 552, 558 (2000). Inferences drawn from the evidence “need only be reasonable and possible, not necessary or inescapable.” Commonwealth v. Arroyo, 442 Mass. at 140. There was testimony that Cheromcka took soda money and that the district did not receive it from her. Viewing the evidence and all reasonable inferences in the light most favorable to the Commonwealth, the evidence was sufficient to permit a rational jury to conclude that Cheromcka stole the soda money.
II. Admission of opinion testimony. Karen Roberts, the certified public accountant and certified fraud examiner retained by [786]*786the district to examine the district’s records, testified at trial about her investigation and findings. Cheromcka claims error in the admission of certain of her testimony in four respects: (1) Roberts was not qualified as an expert witness and could only give percipient testimony as a lay witness; (2) even if the judge impliedly qualified Roberts as an expert witness, her testimony exceeded the scope of permissible expert testimony; (3) Cheromcka’s testimony regarding the amount deposited to Cheromcka’s bank account coupled with her testimony as to the amount missing from the petty cash fund over the same period was unfairly prejudicial; and (4) the judge failed to give the jury adequate instructions regarding expert testimony. Because Cheromcka did not object at trial to Roberts’s testimony, our review is limited to ascertaining whether any of her claims of error gives rise to a substantial risk of a miscarriage of justice. See Commonwealth v. Colon, 64 Mass. App. Ct. 303, 311 (2005).
Cheromcka’s first contention fails for the reason, if no other, that Roberts testified as to her extensive credentials and substantial experience in auditing school districts and was impliedly determined by the judge to be qualified to testify as an expert witness as to matters within her area of expertise. See Commonwealth v. Boyd, 367 Mass. 169, 183 (1975); Commonwealth v. Rivera, 425 Mass. 633, 644 (1997). “ ‘The crucial issue,’ in determining whether a witness is qualified to give an expert opinion, ‘is whether the witness has sufficient “education, training, experience and familiarity” with the subject matter of the testimony.’ ” Commonwealth v. Richardson, 423 Mass. 180, 183 (1996), quoting from McLaughlin v. Selectmen of Amherst, 422 Mass. 359, 361-362 (1996).
In challenging Roberts’s testimony as having exceeded permissible bounds, Cheromcka maintains that the testimony (to the effect that it was “unusual” for a petty cash fund to contain a large amount of money, and for an employee to contribute her own funds for two years) was impermissible opinion concerning the ultimate issue of Cheromcka’s guilt. An expert may testify as to matters not within the jury’s common knowledge or common experience if such testimony will “assist the trier of fact in determining a fact in issue or in understanding the evidence.” [787]*787Commonwealth v. Miranda, 441 Mass. 783, 792-793 (2004). While an expert witness may not directly express her views on a defendant’s guilt, her testimony may “touch[] on the ultimate issue of the case” as long as it is within her field of expertise. Commonwealth v. Tanner, 45 Mass. App. Ct. 576, 579 (1998). The common business practices of a school district, such as the amount usually contained in a petty cash fund and contributions made thereto by educational administrators, are not matters within the common experiences of jurors. Grounded in previously admitted evidence as to the facts of the case at hand, the complained of opinions were permissible explanations on topics within Roberts’s area of expertise. See ibid.
Cheromcka also attacks as unfairly prejudicial Roberts’s analysis of Cheromcka’s deposits to her personal bank account, claiming that Roberts’s determinations as to whether deposits were from “known” or “unknown” sources constituted impermissible opinions. The jury had before them evidence that receipts documenting expenditures from the petty cash fund totaled approximately $69,000; they also had testimony of cash deposits into Cheromcka’s personal account totaling roughly $55,000. Roberts testified as to how she had accounted for all the known deposits and resolved all doubtful cases in Cheromcka’s favor. The analysis of bank deposits is normally outside the common experience of jurors; Roberts’s testimony served to explain the origin of the amount in Cheromcka’s account. See id. at 581. The jury were free to make what they would of the purported correlation between the amount missing from the petty cash fund and the money not otherwise accounted for in Cheromcka’s bank account. Records of the petty cash fund account and Cheromcka’s bank account were in evidence for the jury to examine; the jury could give Roberts’s opinions whatever weight they deemed appropriate.
As to Cheromcka’s contention that the judge failed to give proper jury instructions on how to evaluate expert testimony, where Cheromcka did not request such an instruction, its absence did not create a substantial risk of a miscarriage of justice. See Commonwealth v. Rivera, supra at 645. The purpose of instructions on expert testimony is to remind the jury that they are the sole judges of credibility; a standard instruction to [788]*788that effect as to all witnesses, as was given here, is sufficient. See ibid. See also Commonwealth v. Richardson, supra at 185.21
Judgments affirmed.