SOLUTION: On his way home from the school board meeting, Kevin fills up his car. He likes the idea of using gasoline with ethanol but thinks his car can only handle 25% ethanol. At the gas s

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: On his way home from the school board meeting, Kevin fills up his car. He likes the idea of using gasoline with ethanol but thinks his car can only handle 25% ethanol. At the gas s      Log On


   

Question 1183227: On his way home from the school board meeting, Kevin fills up his car. He likes the idea of using gasoline with ethanol but thinks his car can only handle 25% 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 Kevin use if he wants to fill up his car with 10 gallons of fuel containing 25% ethanol?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
v gallons of the 85% ethanol
10-v gallons of the 10% ethanol

85v%2B10%2810-v%29=25%2A10
-
17v%2B2%2810-v%29=50
17v-2v%2B20=50
15v=30
highlight%28v=2%29
.
.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative method for solving 2-part mixture problems like this, if a formal algebraic solution is not required.

You are mixing 10% ethanol and 85% ethanol, and you want to get 25% ethanol.
Look at the three percentages on a number line and observe/calculate that 25% is 1/5 of the way from 10% to 85%. (10 to 85 is a difference of 75; 10 to 25 is a difference of 15; 15/75 = 1/5.)
That means 1/5 of the mixture needs to be the higher percentage ingredient.

ANSWER: 1/5 of 10 gallons, or 2 gallons, of the 85% ethanol; the other 8 gallons of 10% ethanol.

CHECK:
.85(2)+.10(8) = 1.7+.8 = 2.5
.25(10) = 2.5