Question

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Answer 1

Answer:

a) No because the gallons and quarts of oil you and your friend bought is proportional.

b) Yes because the gallons and quarts of oil are no longer proportional.

c) 1 gallon of gasoline = $3.55

   1 quart of oil = $5.00

Step-by-step explanation:

Let g = cost per gallon of gasoline

Let q = cost per quart of oil

a)  Creating expressions from the given information:

10g + 2q = 45.50

5g + q = 22.75

From inspection, we can see that if we multiply the second equation by 2, it will give us the first equation.  Therefore, they are proportional and we cannot determine the variables.

b) Creating expressions from the given information:

10g + 2q = 45.50

5g + q = 22.75

8g + 2q = 38.40

From inspection, we can see that the third equation is not proportional to equations 1 and 2.  Therefore, we can use this equation with either of the other equations to determine the variables.

c)

Using equations 2 and 3 from the previous part (b):

5g + q = 22.75

8g + 2q = 38.40

Rewrite 5g + q = 22.75 to make q the subject:

⇒ q = 22.75 - 5g

Substitute into 8g + 2q = 38.40 and solve for g:

⇒ 8g + 2(22.75 - 5g) = 38.40

⇒ 8g + 45.5 - 10g = 38.40

⇒ 2g = 7.1

⇒ g = 3.55

Substitute found value for g into q = 22.75 - 5g and solve for q:

⇒ q = 22.75 - (5 x 3.55)

⇒ q = 5