SOLUTION: Amy baked 18 more banana cakes than butter cakes. After giving away 35 cakes of each type, the number of butter cakes left is 3/4 of the number of banana cakes left. How many butte

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Amy baked 18 more banana cakes than butter cakes. After giving away 35 cakes of each type, the number of butter cakes left is 3/4 of the number of banana cakes left. How many butte      Log On


   

Question 1189204: Amy baked 18 more banana cakes than butter cakes. After giving away 35 cakes of each type, the number of butter cakes left is 3/4 of the number of banana cakes left. How many butter cakes did she bake?
Answer by ikleyn(53937) About Me  (Show Source):
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Amy baked 18 more banana cakes than butter cakes.
After giving away 35 cakes of each type, the number of butter cakes left
is 3/4 of the number of banana cakes left. How many butter cakes did she bake?
~~~~~~~~~~~~~~~~~ 

Let x be the number of the butter cakes (the unknown value under the problem's question).

Then the number of the banana cakes is (x+18).


Write the proportion for the remaining cakes

    %28x-35%29%2F%28x%2B18-35%29 = 3%2F4,

or

    %28x-35%29%2F%28x-17%29 = 3%2F4,


To solve it, first cross multiply; then simplify

    4(x-35) = 3(x-17)

    4x - 140 = 3x - 51

    4x - 3x  = 140 - 51

       x     =    89.


ANSWER.  89 butter cakes.

Solved.