Question

(a.): For what amount of driving do the two plans cost the same?

(b.):What is the cost when the two plans cost the same time?

Answer 1

write the expression for each plan, and set them equal to each other.

For part a) solve for m.

For part b) substitute the value of m back into each expression.

Answer 2

First plan: 53 + 0.08m

Second plan: 46 + 0.12m

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`\boxed {a)}` Make the two plans equal to each other & solve.

53 + 0.08m = 46 + 0.12m

Subtract 46 from both sides.

7 = 0.04m

Divide both sides by 0.04.

m = 175

Driving 175 miles would make the two plans cost the same.

`\boxed {b)}` Plug 175 into either one of the plans. We'll plug 175 for m into both just to double check :)

First plan: 53 + 0.08m ⇒ 53 + 0.08(175) = 67

Second plan: 46 + 0.12m ⇒ 46 + 0.12(175) = 67

The cost when the two plans cost the same is $67.