Question

Amy will rent a car for the weekend. She can choose one of two plans. The first plan has no initial fee but costs $0.90 per mile driven. The second plan has an initial fee of $75 and costs an additional $0.80 per mile driven. How many miles would Amy need to drive for the two plans to cost the same?

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Answer 1

750mi

Explanation:

x = how many miles

75+0.8x=0.9x

Move all terms containing x to the left side of the equation.

75−0.1x=0

Subtract 75 from both sides of the equation.

−0.1x=−75

Divide each term in −0.1x=−75 by −0.1 and simplify.

x=750

Answer 2

Our two formulas for each plan:

50 (base fee) + .80x (cost per mile) = y (total cost)

.90x (cost per mile) = y (total cost)

We want to find how many miles we have to drive, so solve for x. We're going to plug in y (from equation 2) into the value for y. This is the substitution method.

50+.80x=y

Plugin: 50+.80x = .90x

Add .90x to each side, subtract 50 from each side: .80x -.90x = -50

Simplify: -.10x = -50

Divide: x = -50/-.10 (two negatives make a positive)

x = 500

So this tells us that she has to drive 500 miles to make the plans equal. Let's verify this by plugging in the value we found for x.

499 miles, plan 2 is cheaper.

50 + .80(499) = 449.20

.90(499) = 449.1

500 miles, they are equal

50 + .80(500) = 450

.90(500) = 450

501 miles, plan 1 is cheaper

50 + .80(501) = 450.8

.90(501) = 450.9

Not my work.