Question

How many gallons of a 65 % sugar solution do we need to mix with

114 gallons of a 40 % sugar solution, so that the resulting mixture is a
46 % sugar solution?

Answer 1

You would need 36 gallons of 65% sugar solution

Explanation:

You can always solve these problems with a proportion

The numerator will represent the amount of sugar, the denominator will represent the amount of solution.

First, we have (.4 * 114 = ) 45.6 gallons of sugar.

`(45.6 + 0.65S)/(114 + S)=(46)/(100)\\(4560 + 65S)/(114+S)=46\\4560 + 65S = 46(114 + S)\\4560 + 65S = 5244 + 46S\\19S = 684\\S = 36`