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Question

Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $21.30. The oil change for the other car required 7 quarts of oil and cost $23.80. How much is the labor fee and how much is each quart of oil?

 

Answer 1

There are 2 unknowns (price of oil and labor fee), so you need 2 equations to solve it.

 

Figure out 2 equations. Then isolate one of the variables in equation 1, substitute it into equation 2, and solve. Then use the new known value and plug it into either equation to solve for the other value.

 

For example:

 

Example_equation 1:  x + y = 3

Example_equation 2:  x + 5y = 11

 

Solve for x in Example_equation 1:

x = 3 - y

 

Plug into Example_equation 2:

(3 - y) + 5y = 11

3 + 4y = 8

4y = 8

y = 2

 

Plug y = 2 into Example_equation1:

x + 2 = 3

x = 1

 

I'll give you equation 1, and try to find equation 2 from this. Then follow the above steps.

 

Equation 1:  5quarts * x [dollars per quart] + Flat_Labor_Fee = $21.30

Equation 2:  ??