Question

Augustus is trying to make chocolate milk. He has made a 10% chocolate milk solution (this means that the solution is 10% chocolate and 90% milk). He has also made a 25% chocolate milk solution. Unfortunately, the 10% solution is too weak, and the 25% solution is way too chocolaty. He has a whole lot of the 10% solution, but he has only 30 gallons of the 25% solution. How many gallons of 10% solution should he add to the 25% solution to make a mixture that is 15% chocolate?

Answer 1

60 gallons

Explanation:

The amount of 10% solution he should add can be found by writing an equation for the total amount of chocolate in the mix.

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Let x represent the amount of 10% solution that Augustus needs to add to the 30 gallons of 25% solution. The amount of chocolate in the resulting 15% mix is ...

0.10x +0.25(30) = 0.15(x +30) . . . . gallons of chocolate in the mix

0.10(30) = 0.05x . . . . . . . . subtract 0.10x +0.15(30)

60 = x . . . . . . . . . . . . divide by 0.05

Augustus should add 60 gallons of the 10% solution to make a 15% mixture.