Chapter P, Problem 29E

The Advantage Cash Card At the student union on a certain campus, you can save on food purchases by using the Advantage Cash Card. You deposit money into an Advantage Cash account and are issued a credit card the you use to purchase food. The card has several advantages:

♣ If you open your Advantage Cash account for $\$200$ or more, a $5\%$ bonus is added to your account balance.

♣ When you use your Advantage Cash Card, you receive $5\%$ off the retail price of any food purchase.

♣ When you buy food with cash, you must pay a sales tax of $7.375\%$. With the Advantage Cash Card, you pay no sales tax.

a. An item retails for $\$1.00$. What do you pay if you use your Advantage Cash Card?

b. An item retails for $\$1.00$. What do you pay if you use cash? Round your answer to five decimal places for use in part d.

c. What retail value of food will you be able to purchase if you open an Advantage Cash account for $\$300$? (Suggestion: Don’t forget your $5\%$ bonus and use the results of part a)

d. What retail value of food would you be able to purchase with $\$300$ if you spend it as cash at the food court? (Suggestion: Use the results of part b)

e. Calculate the percentage increase from your answer for part d to your answer for part c. Explain in practical terms the meaning of this percentage.