Question

Ace car rental advertises that a rental car costs $25 per day plus a charge of 10 cents per mile. For the same car, Better Car rental advertises a price of $40 per day plus 5 cents per mile. What number of mile is the cost of renting a car the same at both companies ?

Answer 1

Let's say you drive x miles.
For Ace car rental, how much will the x miles cost you?
For better car rental, how much will the x miles cost you?

Answer 2

Ace car rental 10 cents per mile and Better car rental 5 cents per mile.

Answer 3

Right.
Now if you drive x miles, how much will that cost?

Answer 4

It's asking what number of miles is the cost of renting a car the same at both companies.

Answer 5

This is what I mean

For Ace car rental:
1 mile costs 0.10 * 1
2 miles cost 0.10 * 2
x miles cost 0.01 * x = 0.10x = 0.1x

For Better car rental:
1 mile costs 0.05 * 1
2 miles cost 0.05 * 2
x miles cost 0.05 * x = 0.05x

Answer 6

Now that we know how much driving x miles will cost with each car rental company, we need to look at how much the total cost of each rental company will be.

Ace charges $25 per day.
That means one day plus x miles would cost
25 + 0.1x.

Better charges $40 per day
That means one day plus x miles would cost
40 + 0.05x.

Do you follow so far?

Answer 7

yes - but I don't know how to come up with how may miles for each company would be the same.

Answer 8

We're getting there.

Answer 9

Now notice the question we are asked.
"What number of miles is the cost of renting a car the same at both companies?"

Answer 10

okay

Answer 11

Since we know it costs 25 + 0.1x at Ace and 40 + 0.05x at Better, and we want the costs to be the same, we set the costs equal to each other.

25 + 0.1x = 40 + 0.05x

Now we have an equation with only one unknown which we can solve. Also, notice the unknown is x which from the beginning we let it be the number of miles.

Answer 12

Now we solve this equation.

25 + 0.1x = 40 + 0.05x

Answer 13

Let's subtract 0.05x from both sides:

25 + 0.05x = 40

Now let's subtract 25 from both sides:

0.05x = 15

Now we divide both sides by 0.05

x = 300

The answer is 300 miles.

Answer 14

Gosh !! Thanks so much !!!!!

Answer 15

Now we check the answer.

Ace: 25 + 0.1x = 25 + 0.1(300) = 25 + 30 = 55 ($55 for 1 day and 300 miles).
Better: 40 + 0.05x = 40 + 0.05(300) = 40 + 15 = 55 ($55 for 1 day and 300 miles).

Our answer is correct. When driving 300 miles, both rental places cost $55 for 1 day.

Remember, the answer is 300 miles, not $55, since we were asked how many miles would it take to cost the same. We were not asked what the actual cost would be.

Answer 16

You're welcome.

Answer 17

How about this one - If y =(x+3)2, then (-2x-6)2 would equal what?