Answer :
The two plans costs the same for 450 miles
The cost when the two plans costs the same is $116.5
Step-by-step explanation:
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
We need to know for what amount of driving do the two plans costs
the same
Assume that the amount of driving is x miles
∵ The amount of driving = x miles
First 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 miles
The two plans costs the same for 450 miles
Substitute 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 = $116.5
The cost when the two plans costs the same is $116.5
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