How many cups of the batter and chocolate chip mixture will she require?

Question

Alonda is making triple chocolate chip cookies. She has a batter that is 20% chocolate and a chocolate chip mixture that is 50% milk Chocolate chips. She needs 10 cups of the mixture and wants the final cookies to be 26% chocolate. 

Answer 1

We can solve this problem by making a table, where x = cups of batter and 10 - x = cups of chocolate chip mixture (since, altogether, Alonda wants 10 cups). The first row represents the batter, the second row represents the chocolate chip mixture, and the third row represents the final cookies:

 

CUPS         CHOCOLATE CONCENTRATION         AMOUNT OF CHOCOLATE

x                         0.2                                                   0.2x

10 - x                0.5                                                   0.5(10 - x)

10                    0.26                                                  0.26(10)

 

So, for Alonda's mixture to work out correctly, she needs the amount of chocolate in the batter plus the amount of chocolate in the chocolate chip mixture to equal 0.26(10):

 

0.2x + 0.5(10 - x) = 0.26(10)

0.2x + 5 - 0.5x = 2.6

-0.3x + 5 = 2.6

-0.3x = -2.4

x = 8

 

That means Alonda needs 8 cups of batter and 10 - 8 = 2 cups of chocolate chip mixture.