Christopher likes cupcakes (C) and muffins (M). His preferences can be represented by the utility function U(C, M) = C0.5M0.5. He received a gift basket with 16 cupcakes and 4 muffins, but when he was about to eat them, he found out his younger brother Dan had eaten 14 cupcakes and 2 muffins. Christopher made Dan buy what he'd eaten back. However, the bakery was out of muffins and Dan only bought cupcakes. How many cupcakes did Dan buy if, in addition to what he had not eaten from the basket, the new cupcakes provide Christopher with the same level of utility as the original gift basket?

Kiona co. set up a petty cash fund for payments of small amounts. the following transactions involving the petty cash fund occurred in may (the last month of the company's fiscal year). may 1 prepared a company check for $350 to establish the petty cash fund. 15 prepared a company check to replenish the fund for the following expenditures made since may 1. a. paid $109.20 for janitorial services. b. paid $89.15 for miscellaneous expenses. c. paid postage expenses of $60.90. d. paid $80.01 to the county gazette (the local newspaper) for an advertisement. e. counted $26.84 remaining in the petty cashbox. 16 prepared a company check for $200 to increase the fund to $550. 31 the petty cashier reports that $380.27 cash remains in the fund. a company check is drawn to replenish the fund for the following expenditures made since may 15. f. paid postage expenses of $59.10. g. reimbursed the office manager for business mileage, $47.05. h. paid $48.58 to deliver merchandise to a customer, terms fob destination. 31 the company decides that the may 16 increase in the fund was too large. it reduces the fund by $50, leaving a total of $500.