Mathematics: 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?

How many gallons of a 65 % sugar solution do we

michelle7511

02.01.2022

You would need 36 gallons of 65% sugar solution

Step-by-step 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.

$\frac{45.6 + 0.65S}{114 + S}=\frac{46}{100}\\\frac{4560 + 65S}{114+S}=46\\4560 + 65S = 46(114 + S)\\4560 + 65S = 5244 + 46S\\19S = 684\\S = 36$

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