An automobile engine can run on a mixture of gasoline and a substitute fuel. If gas costs $3.40 per gallon and the substitute fuel costs $2.....

Question

An automobile engine can run on a mixture of gasoline and a substitute fuel. If gas costs $3.40 per gallon and the substitute fuel costs $2 per gallon, what percent of a mixture must be substitute fuel to bring the cost down to $2.98 per gallon?

Answer 1

A common way to solve word problems in algebra is with a system of equations. With a system of equations, you can solve for two unknown variables with two known equations. In our case, we're looking to write two equations so that we can find the right amounts to get the price to $2.98 per gallon.

Using the fact that we know the price per gallon of the two fuels and the target price per gallon, we can write the equation:

$3.40·g + $2·s = $2.98

Where g is the percent of gas and s is the percent of substitute in the mix.

This equation alone isn't enough to solve. We also know a simple fact about percentages: if we're looking to fill a container, 100% of the tank will be filled, or written in a decimal, 1.00 full tank. In the full tank, there is going to be a certain percent gas and certain percent substitute, which is currently unknown. With this fact, we can write the equation:

g + s = 1.00

Where g is the percent of gas and s is the percent of substitute in the mix.

We can now solve the system of equations to get our percents:

g = 1.00 - s solve for g

3.40·(1.00 - s) + 2·s = 2.98 substitute g into the first equation

s = 0.3 distribute the term and solve for s

g + 0.3 = 1.00 substitute s into the second equation

g = 0.7 solve for g

We can answer the question:

0.7 or 70% of the mix should be regular gas and 0.3 or 30% should be the substitute gas