Solve the problem.
-Two different gasohol mixtures are available. One contains $5 \%$ alcohol and the other $12 \%$ alcohol. How much of each should be mixed to obtain $500 \mathrm { gal }$ of gasohol containing $10 \%$ alcohol?
A) 357 gal 5% ; 357 gal 12%
B) 25 gal 5% ; 60 gal 12%
C) 143 gal 5% ; 357 gal 12%
D) 208 gal 5% ; 292 gal 12%

Question

Quizplus · Accepted Answer

To solve this, we use the method of weighted averages. Let $x$ be the amount of 5% alcohol mixture and $y$ be the amount of 12% alcohol mixture. We have two equations:1. $x + y = 500$ (the total mixture is 500 gallons)2. $0.05x + 0.12y = 0.10 \times 500$ (to get a 10% alcohol mixture from the total 500 gallons)Solving these equations, we find $x = 143$ and $y = 357$, meaning 143 gallons of the 5% mixture and 357 gallons of the 12% mixture are needed.

Solve the Problem 5%5 \%5% Alcohol and the Other 12%12 \%12% Alcohol How Much of Each Should Be Mixed to Obtain

Solve the Problem $5 \%$ Alcohol and the Other $12 \%$ Alcohol How Much of Each Should Be Mixed to Obtain