Question

Suppose AAA charges $30 and 25 cents per mile to tow your vehicle. Sandy's charges $10 and 35 cents per mile. For what number of miles will the two companies be the same?

Answer 1

The number of miles where AAA's and Sandy's towing charges are equal, we set up the equation based on their rates and solve for the miles, which results in 200 miles.

Step-by-step explanation:

To determine the number of miles for which the towing charges by AAA and Sandy's would be the same, we need to set up an equation based on the given rates. Let's denote the number of miles as m.

AAA's charges can be represented as $30 + 0.25m, and Sandy's as $10 + 0.35m. By setting these two expressions equal to each other, we get the equation:

30 + 0.25m = 10 + 0.35m

Now, let's solve for m:

1. Subtract 10 from both sides: 20 + 0.25m = 0.35m
2. Subtract 0.25m from both sides: 20 = 0.10m
3. Divide both sides by 0.10: m = 200

Thus, the number of miles at which the charges from both companies will be the same is 200 miles.