Question

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 gal of gasohol containing 10% alcohol?

Answer 1

Answer:

The volumes of two different gasohol mixtures available are 142.86 gal and 357.14 gal

Explanation:

let the two mixtures be x and y respectively

The two mixtures must sum up to 500 gal of gasohol:

x + y = 500 ---------equation 1

The two mixtures must contain 5% alcohol and 12% alcohol  and must be equal to 10% of the total mixture

0.05x + 0.12y = 0.1*500

0.05x + 0.12y = 50 ---------equation 2

from equation (1); y = 500-x

substitute in y into equation 2

0.05x + 0.12(500-x) = 50

0.05x + 60 -0.12x = 50

-0.07x = -10

x = 142.86 gal

y = 500-142.86 = 357.14 gal

Therefore,  the volumes of two different gasohol mixtures available are 142.86 gal and 357.14 gal.