MATH HELP!!!!!!!!!

Question

An oil change service center charges $42 for an oil change plus 6 quarts of oil. Another

option is $26 for an oil change plus 2 quarts of oil. Use a system of equations to find

how much an oil change is and how much a quart of oil is.

Answer 1

Let c = the cost of the oil change and q = the price of a quart of oil.

c + 6q = 42

c + 2q = 26

Subtract the two equations to eliminate c:

4q = 16

q = $4

c + 2(4) = 26

c = 26 - 8 = $18

An oil change is $18 and the price of a quart of oil is $4.

Answer 2

Let's first create define some variables: c will be cost of oil change and q will be cost of a quart of oil.

One equation we can write is 42 = c + 6q

Second equation: 26 = c + 2q

Now, let's rearrange the terms in equation 2 to get: 26 - 2q = c

Then substitute that expression into equation 1: 42 = (26 - 2q) + 6q

Simplify: 42 = 26 + 4q

16 = 4q

4 = q

So now we know the cost of a quart of oil: $4

We plug that cost into our rearranged equation 2: 26 - 2(4) = c

Simplify: 18 = c

Ultimately we find the cost of an oil change to be $18 and the cost of a quart of oil to be $4

Answer 3

MATH HELP!!!!!!!!!

An oil change service center charges $42 for an oil change plus 6 quarts of oil. Another

option is $26 for an oil change plus 2 quarts of oil. Use a system of equations to find

how much an oil change is and how much a quart of oil is.

===========

Let O = Oil Change Amount

Let Q = Price of a quart of oil.

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option 1 ..... O + 6 Q = $42

option 2...... O + 2 Q = $26

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O = $42 - 6Q

O = $26 - 2Q

----

$26 - 2Q + 6Q = $42

-26 -26

-2Q + 6Q = 16

4Q = 16.......Q = $4.................check.........O = 26 - 2(4) = $18.......so Quart of Oil = $4 and Oil Change = $18

check option 1.......O + 6 Q = $42.....$18 + 6($4) = ?? $24 + $18 = $42....that checks...

check option 2.......O + 2 Q = $26.....$18 + 2($4) = ?? $18 + $8 = $26......that checks..