What was the total number of eggs used to make all 3 kinds of cakes in the following problem:

Last week the Star Bakery made 3 kinds of cakes, one half of the cakes were made with 4 eggs each, two thirds of the rest of the cakes were made with 3 eggs each, and the remaining 54 cakes were made with 2 eggs each. What was the total number of eggs used to make all of these cakes?

Expert Answers

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According to the problem Star Bakery made 3 kinds of cakes; let the total number of cakes made be C.

One half of the cakes were made with 4 eggs each, C/2 cakes required 2 eggs. This gives the number of eggs used as 4*C/2.

Two thirds of the rest of the cakes were made with 3 eggs each. This gives the number of eggs used as (2/3)*(C/2)*3.

And the remaining 54 cakes were made with 2 eggs each. This gives the number of eggs used as 54*2.

From the information we get 54 = C - C/2 - C/3

=> C = 324

The total number of eggs used is 54*2 + (2/3)*(324/2)*3 + 4*324/2

=> 1080

The total number of eggs used is 1080.

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