Trey mechanic will fix Trey's car at a rate of $20 per hour, plus $400 for the cost of a part. Trey's neighbor already has the needed part and will fix the car for only $70 per hour. For how many hours will the cost of having the car fixed by either person be the same?

8 hours.

Step-by-step explanation:

let x represent number of hours.

We have been given that Trey mechanic will fix Trey's car at a rate of $20 per hour, plus $400 for the cost of a part.

So total cost of repairing a car for x hours by Trey mechanic would be .

We are also told that the neighbor has the needed part and will fix the car for only $70 per hour. So total cost of repairing a car for x hours by neighbor would be .

To find the number of hours, when the cost of fixing the car by either person will be equal, we need to equate both expressions as:

Let us solve for x.

Therefore, after 8 hours the cost of having the car fixed by either person will be the same.

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d