Question

Please explain how to do this i need to show my work

Answer 1

Answer:

labor fee: $15.15, quart of oil: $1.25

Step-by-step explanation:

You solve this by setting up two equations, one for each car.

First we have to define what variables we need and what they mean.

To be solvable, you need as many equations as you have variables.

Let's call the labor fee x and the cost of oil per quart y.

This means we'll be needing two equations to have any chance of solving this. Since we have one equation per car, this looks promising!

Car 1: x + 5y = 21.4

Car 2: x + 7y = 23.9

To solve these, you combine them into one equation by eliminating one variable:

Rewriting the first: x = 21.4 - 5y

So, we can substitute 21.4 - 5y for x in the second. Then we have an equation with only y:

21.4 - 5y + 7y = 23.9

2y = 23.9-21.4 = 2.5

y = 1.25

Plugging this value back into the rewritten first gives us the labour fee:

x = 21.4 - 5*1.25 = 15.15