Question

The octane rating of a gasoline is a measure of the amount of isooctane in the gas. Subaru recommends 91-octane gasoline for 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?

Answer 1

Let x = gallons of 87 octane gas
Let y = gallons of 91 octane gas

Next, you need to set up some relationship to express the constraints.

Hint: cx + ky / (c + k) is a weighted average that can be used in this problem.

Answer 2

Since you are logged off, I'll proceed with the next step.

x + y = 12

We know that together, x + y must equal 12 gals.

Next, we need to think about a mixture that gets us to 91 octane.

To do this, we'll use the weighted average mentioned earlier.

(87x + 93y)/(x + y) = 91
87x + 93y = 91x + 91y
-4x + 2y = 0

So:
x + y = 12
-4x + 2y = 0

Two equations, two unknowns. Solve.

6y = 48 -> y = 8
x = 4

So, 4 gallons of 87 octane gas, and 8 gallons of 93 octane gas will get us the desired octane.