SOLUTION: How much 78 octane gas and 91 octane gas should be blended to make 13 gallons of 87 octane gas?

Question 1102648: How much 78 octane gas and 91 octane gas should be blended to make 13 gallons of 87 octane gas?
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I will hope you get other responses from other tutors showing the classic method for solving "mixture" problems like this. I use a different method which is much faster and easier.

Think of three numbers on a number line: the 78 and 91 octane of the two fuels being mixed, and the 87 octane of the mixture.

The 87 is 9/13 of the way from 78 to 91. (91-78 = 13; 87-78 = 9)

That means 9/13 of the mixture must be the 91 octane, with the rest being the 78 octane.

The amount of the mixture is 13 gallons; 9/13 of 13 gallons is 9 gallons.

You need to mix 9 gallons of the 91 octane with 4 gallons of the 78 octane to get 13 gallons of 87 octane.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
x, gallons of 78% octane fuel
13-x, gallons of 91% octane

-

------------ 4 gallons of 78 octane
----------------9 gallons of 91 octane
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