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.
