An SUV costs $27,070 and costs an average of $0.18 per mile to maintain. A hybrid model of the SUV costs $32,880 and costs an average of $0.13 per mile to maintain. After how many miles will the cost of the gas-only SUV exceed the cost of hybrid?

Question

Mathematics

Matthew Jennings

22 August, 08:13

An SUV costs $27,070 and costs an average of $0.18 per mile to maintain. A hybrid model of the SUV costs $32,880 and costs an average of $0.13 per mile to maintain. After how many miles will the cost of the gas-only SUV exceed the cost of hybrid?

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Answers (1)

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Morgan Mccoy · Answer 1

116,200 km

Step-by-step explanation:

Here we have 2 cars, each one with it's corresponding costs. Let's write each cost as functions. The SUV costs $27,070 plus $0.018 per mile. Let x be the miles and SUV (x) the SUV's cost:

SUV (x) = 27070+0.18x

We can do the same for the hybrid with a cost function H (x):

H (x) = 32880+0.13x

We now need the cost of the SUV to be greater than the hybrid. This is SUV (x) > H (x):

27070+0.18x > 32880+0.13x

Let's subtract 27070 in each side:

0.18 x > 32880 - 27070 + 0.13x

Now let's subtract 0.13x in both sides:

0.05x > 5810

Divide both by 0.05:

x > 5810/0.05

x > 116,200

So, after 116,200km the SUV will turn to be more expensive.