Question

On his way home from the school board meeting, Keith fills up his car. He likes the idea of using gasoline with ethanol, but thinks his car can only handle 40% ethanol. At the gas station, he can use regular gas with 10% ethanol or E85 fuel with 85% ethanol.

How many gallons of each type of fuel should Keith use if he wants to fill up his car with 10 gallons of fuel containing 40% ethanol?

a. 6 gallons of regular gas with 10% ethanol; 4 gallons of E85 fuel with 85% ethanol
b. 4 gallons of regular gas with 10% ethanol; 6 gallons of E85 fuel with 85% ethanol
c. 2 gallons of regular gas with 10% ethanol; 8 gallons of E85 fuel with 85% ethanol
d. 8 gallons of regular gas with 10% ethanol; 2 gallons of E85 fuel with 85% ethanol

Answer 1

a. 6 gallons of regular gas with 10% ethanol; 4 gallons of E85 fuel with 85% ethanol

Explanation:

let G be gasohol or E10 gallons

let E be E85 gallons

G + E = 10

G = 10 - E

G(10) + E(85) = 10(40)

( 10 - E)(10) + E(85) = 10(40)

100 - 10E + 85E = 400

75E = 300

E = 4 gallon

G = 10 - 4 = 6 gallon