7. Shirley has a cupcake business. Her business sells gourmet cupcakes to corpor

Question

7. Shirley has a cupcake business. Her business sells gourmet cupcakes to corporate clients to serve at their special events. One Friday morning she had 10,080 cupcakes ready to be delivered to a lot of clients. Each client was scheduled to receive the same amount of cupcakes. But just before delivery was to commence, four clients called and canceled. Rather than throwing away a bunch of cupcakes, Shirley deci- ded to add 60 cupcakes to each of the other orders. So every remaining client got 60 more cupcakes than they would have received originally. How many cupcakes did each corporate client end up getting?

Explanation / Answer

Shirley had 10,080 cup cakes that were to be delivered to 'n' clients such that each would receive an equal number of cup cakes given by : 10080/n

But 4 clients cancelled and the remaining n-4 clients got 60 extra cup cakes than usual so

10080/n + 60 = 10080/(n-4)

60= 10080/ n-4 - 10080/n

10080n -10080n + 40320/ n(n-4) = 60

n(n-4) = 40320/60 = 672

So n(n-4) = 28*24 = 672. So n= 28 and n-4 = 24 clients received 10080/24 = 420 cup cakes each

Thus, each corporate client ended up getting 420 cup cakes

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