# How much 87 octane gas and and 93 octane gas should Kelsey mix in order to make 12 gallons of 91 octane gas for her car ?I need to show all steps thank you

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Since the desired octane level is not the average of the other two octane levels, we cannot simply mix even amounts. Therefore we need to set up a couple of equations and define some variables.

x = percent of 87 octane gas

y = percent of 93 octane gas

We also know that the percent of each gas must equal 100% (or 1) so

x + y = 1

We can then use the following equation to find the percentage of each type of gas

87x + 93y = 91

Since we have two equations (the last two shown), we have two unknowns but we also have two equations so we can solve for both unknowns.

if x + y = 1; then x = 1-y

This can be substituted into our other equation to get

87(1-y) +93y = 91

therefore

87-87y + 93 y = 91

87 + 6y = 91

6y = 4

y = 0.6667 (percent of the 93 octane gas)

Because x + y = 1, x = 0.3333 (percent of 87 octane gas)

Now multiply the percentages by the total volume of 12 gallons to get the volume of each

volume of 87 octane gas = 0.333 * 12 = 4 gallons

volume of 93 octane gas = 0.667 * 12 = 8 gallons

Thank you.