M31-08

Official Solution:

A baker charges \(x\) dollars for a birthday cake. Next week, she plans to earn 320 dollars by selling cakes. If she were to reduce the price of the cake by 20 percent, she would need to sell two more cakes to generate the same revenue. How many cakes does she plan to sell next week?

A. 2
B. 4
C. 6
D. 8
E. 10


Reducing the price by 20% is equivalent to multiplying the price by \(\frac{8}{10}\). In this scenario, to achieve the same revenue, the baker must sell \(\frac{10}{8}\) times as many cakes. Essentially, we are told that \((\text{number of cakes}) * \frac{10}{8} = (\text{number of cakes}) + 2\), which implies that the number of cakes is 8.

Another way to look at this is by noting that when the price is reduced by 20%, it becomes 4/5th of the original price. To earn the same revenue, she must increase the quantity sold by 25% (the revenue must increase by 5/4 times to compensate for the reduction in price to 4/5th). From the question, we know that 25% of the original quantity equals 2. Thus, the total original quantity is 2 * 4 = 8.


Answer: D