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Question

Deshaun will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $46

and costs an additional $0.12 per mile driven. The second plan has an initial fee of $51 and costs an additional $0.08 per mile driven.

For what amount of driving do the two plans cost the same?\

What is the cost when the two plans cost the same?

Answer 1

These are the basic equations needed for this problem:

Total cost = Fixed cost + variable cost

Cost Plan 1 = Cost Plan 2

Let x = Number of miles driven

46+.12x=51+.08x Subtract 0.08x from both sides

46+.12x-.08x=51+.08x-.08x Simplify

46+.04x=51 Subtract 46 from both sides

46+.04x-46=51-46 Simplify

.04x=5 Divide both sides by .04

.04x/.04=5/.04

x=125 miles driven means the cost will be the same for both plans

To find the cost, plug in x to one of the equations.

46+.12(125)

46+15

$61 will be cost when both cars are driven 125 miles

Answer 2

the first expression: 46+0.12x

the second expression: 51+0.08x

Now we can use both expressions to make an equation and we can the solve for x

46+0.12x=51+0.08x (this is our original equation)

0.12x−0.08x=51−46 (combine like terms)

.04x = 5 (we subtract both sides of the equation 0.12x−0.08x=.05 and 51−46=5)

.04x÷.04=x and 5÷.04=125 (divide both sides of the equation by .04)

x=125