Chris would need to drive 650 miles for the two plans to cost the same.
Further Explanation:
Let d = distance traveled in miles
Plan 1 will have an initial fee of $65 and a cost of $0.80 per mile driven. Therefore, the total cost to drive a distance of d will be:
total cost = $65 + ($ 0.80 × d)
Plan 2 will have no initial fee but has a cost of $0.90 per mile drive. The total cost, then, to drive a distance of d will be:
total cost = $0.90 × d
If the two costs are the same, then:
$65 + ($ 0.80 × d) = $0.90 × d
The distance driven, d, can then be solved algebraically.
Combining like terms:
$65 = $0.90d - $0.80d
$65 = $0.10d
Solving for d:
d = $65/$0.10
d = 650 miles
To check the answer, solve for the total cost of Plan 1 and Plan 2 and see if they are equal.
Plan 1:
total cost = $65 + ($0.80 x 650)
total cost = $65 + $520
<u>total cost = $585</u>
Plan 2:
total cost = $0.90 x 650
<u>total cost = $585</u>
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Since both plans cost the same, then the distance 650 mi is correct.
Learn More
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Keywords: word problem, total cost
