The missing part of the question is "For what amount of driving do the two plans cost the same"
The amount of driving that do the two plans cost the same is 450 miles
Step-by-step explanation:
Isabel will rent a car for the weekend. She can choose one of two plans
- The first plan has an initial fee of $46 and costs an additional $0.13 per mile driven
- The second plan has an initial fee of $55 and costs an additional $0.11 per mile driven
We need to find for what amount of driving do the two plans cost the same
Assume that she will drive for d miles
The first plan:
∵ The initial fee is $46
∵ The additional cost is 0.13 per mile
∵ She will drive for d miles
- The cost of her trip is the sum of $46 and the product of
0.13 and d
∴ The cost = 46 + 0.13 d ⇒ (1)
The second plan:
∵ The initial fee is $55
∵ The additional cost is 0.11 per mile
∵ She will drive for d miles
- The cost of her trip is the sum of $55 and the product of
0.11 and d
∴ The cost = 55 + 0.11 d ⇒ (2)
∵ The cost of the two plans is the same
- Equate (1) and (2) to find d
∴ 46 + 0.13 d = 55 + 0.11 d
- Subtract 46 from both sides
∴ 0.13 d = 0.11 d + 9
- Subtract 0.11 d from both sides
∴ 0.02 d = 9
- Divide both sides by 0.02
∴ d = 450
The amount of driving that do the two plans cost the same is 450 miles
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