Final answer:
To get a mixture that is 12% ethanol, you need to mix 35 gallons of the 14% ethanol fuel mixture with 10 gallons of the 5% ethanol fuel mixture.
Step-by-step explanation:
To solve this problem, we can set up an equation based on the given information:
Let x be the amount of 14% ethanol fuel mixture needed. The equation is:
(0.14x + 0.05 * 10) / (x + 10) = 0.12
Multiply both sides of the equation by (x + 10) to eliminate the denominator:
0.14x + 0.05 * 10 = 0.12 * (x + 10)
Simplify the equation:
0.14x + 0.5 = 0.12x + 1.2
Combine like terms:
0.02x = 0.7
Divide both sides of the equation by 0.02:
x = 35
Therefore, you need 35 gallons of the 14% ethanol fuel mixture.