Question

Company a charges an $80 fee to rent a truck and $12 per mile. Another rental company charges a $150 fee to rent a truck and $8.50 per mile. The two rental companies will cost the same amount at how many miles?

Answer 1

Setting the total cost equations from both companies equal to each other and solving for the number of miles, we find that the two rental companies will cost the same amount at 20 miles.

Step-by-step explanation:

To find at how many miles the cost of renting a truck would be the same for both companies, we set up an equation where the total cost for each company is equal. Let x represent the number of miles driven. For Company A, the cost is $80 plus $12 per mile, which gives us an equation 80 + 12x. For Company B, the cost is $150 plus $8.50 per mile, represented as 150 + 8.5x. Setting these two expressions equal to each other gives us the equation:

80 + 12x = 150 + 8.5x

To solve for x, we combine like terms:

12x - 8.5x = 150 - 80

3.5x = 70

We then divide both sides by 3.5 to isolate x:

x = 70 / 3.5

x = 20

So, the two rental companies would charge the same amount when a truck is driven for 20 miles.