MATH SOLVE

4 months ago

Q:
# Lena will rent a car for the weekend. She can chose one of two plans. The first plan has an initial fee of $49.00 and costs and additional $0.15 per mile driven. The second plan has an initial fee of $40.00 and cost an additional $0.17 per mile driven. For what amount of driving do the two plans costs the same? What is the cost when the two plans costs the same?

Accepted Solution

A:

The two plans costs the same for 450 milesThe cost when the two plans costs the same is $116.5Step-by-step explanation:Lena will rent a car for the weekend. She can chose one of two plansThe first plan has an initial fee of $49.00 and costs and additional $0.15 per mile drivenThe second plan has an initial fee of $40.00 and cost an additional $0.17 per mile drivenWe need to know for what amount of driving do the two plans coststhe sameAssume that the amount of driving is x miles∵ The amount of driving = x milesFirst plan:∵ The initial fee = $49∵ The cost per mile = $0.15∴ The cost of the rent = 0.15 x + 49 ⇒ (1)Second plan:∵ The initial fee = $40∵ The cost per mile = $0.17∴ The cost of the rent = 0.17 x + 40 ⇒ (2)∵ The two plans have the same cost∴ Equate (1) and (2)∴ 0.15 x + 49 = 0.17 x + 40- Subtract 0.15 x from both sides∴ 49 = 0.02 x + 40- Subtract 40 from both sides∴ 9 = 0.02 x- Divide both sides by 0.02∴ x = 450 milesThe two plans costs the same for 450 milesSubstitute x by 450 in (1) or (2) to find the same cost∵ The cost = 0.15 x + 49∵ x = 450∴ The cost = 0.15(450) + 49∴ The cost = $116.5The cost when the two plans costs the same is $116.5Learn more:You can learn more about word problems in brainly.com/question/5248692 #LearnwithBrainly