The octane rating of a gasoline is a measure of the amount of isooctane in the gas. Subaru recommends 91-octane gasoline for the 2008 Legacy 3.0 R. How much 87-octane gas and 93-octane gas should Kelsey mix in order to make 12 gal of 91-octane gas for her Legacy?

Question

anonymous · Answer

well i would say that since 87 is 4 less than 91 and 93 is 2 more than 91 then the ration you would need is 2:1 being 2 gallons of 87 to every 1 gallon of 93. That being said i would guess that it would be 8 gallons of 87 octane fuel and 4 gallons of 93 octane fuel.

anonymous · Answer

ok, well that sounds good. I have been getting different numbers all over the place
guess I could give it a shot

anonymous · Answer

your equation is 
$$87x+93(12-x)=91\times 12$$

anonymous · Answer

or at least that is one way to solve.  reason should be clear.

anonymous · Answer

well wouldn't you need two variables for that?

anonymous · Answer

not at all. if you put in x gallons of 87 octane in your 12 gallon mixture, then the remaining amount for 93 octane must by necessity be12-x

anonymous · Answer

true true

anonymous · Answer

i see no reason to work with a system of equations and then reduce to one equation with one variable when you can use one variable to begin with.  but i guess it is a matter of choice

anonymous · Answer

btw i get x = 4 meaning 4 gallons of 87 octane and therefore 8 of 93 octane.

anonymous · Answer

yes i must have just misthought it but it makes sense since 93 is closer that it would be more of the one closer than the one further away