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. Th

Question

2 years ago

9

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. Th

e oil change for one car required 5 quarts of oil and cost $24.80. The oil change for the other car required 7 quarts of oil and cost $29.30. How much is the labor fee and how much is each quart of oil?

Mathematics

1 answer:

zvonat [6] · Answer 1 · 2022-06-11T04:18:03+03:00

The labor fee is $13.55 and each quart of oil is $2.25

Step-by-step explanation:

Let,

x be the amount of each quart of oil

y be the amount of labor fee

According to given statement;

5x+y=24.80 Eqn 1

7x+y=29.30 Eqn 2

Subtracting Eqn 1 from Eqn 2

$(7x+y)-(5x+y)=29.30-24.80\\7x+y-5x-y=4.50\\2x=4.50$

Dividing both sides by 2

$\frac{2x}{2}=\frac{4.50}{2}\\x=2.25$

Putting x=2.25 in Eqn 1

$5(2.25)+y=24.80\\11.25+y=24.80\\y=24.80-11.25\\y=13.55$

The labor fee is $13.55 and each quart of oil is $2.25

Keywords: linear equation, subtraction

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