Ben charges $15.50 to rent bikes/helmets per hour, Cathie charges $9.25 per hour for bikes & a $12.50 flat rate for helmets.

Question

I need to find how many hours are the total charges at both shops the same?

Answer 1

the purpose of a question such as this is to show that you will spend more at Cathie's if you rent for a small number of hours but you will spend more at Ben's if you rent for many hours. But there is a value for the number of hours you rent where the cost is the same at both places. I f you know this value and you know how many hours you want to rent, then you can figure out which place will give you a better deal.

 

Let h = hours you want to rent

 

cost at Ben's is 15.50h

cost at Cathie's is 9.25h + 12.50

 

Again, the question is when are the costs the same.

 

Therefore    15.50h = 9.25h + 12.50     and solve for h

 

6.25h = 12.50

 

h = 2 hours

 

So if you want to rent for 1 hour, go to Ben's

2 hours, it doesn't matter as far as cost is concerned

More than 2 hours, go to Cathie's

Answer 2

One unknown is the number of Total Cost.

Two others are number of hours at each shop.

The total cost at Ben's is:  Cost_B = $15.50 x H_B

The total cost at Cathie's is: Cost_C = ($9.25 x H_C) + $12.50

The total cost are the same so:

Cost_B = Cost_C

$15.50 x H_B = ($9.25 x H_C) + $12.50

 

The problem here is you want to know when the total costs are the same.

You need another equation since you have multiple unknowns.

Nothing in your problem gives another equation.

 

UNLESS do you want to know the number of hours For Which the total charges are the same?

You didn't really say that in your question, but maybe that is what you mean.

Then you can say H_B = H_C = Hrs

And the equation becomes:

$15.50 x Hrs = ($9.25 x Hrs) + $12.50

and you can solve for Hrs.

 

If that is what you meant, then either you, the teacher, or the book

should have been more careful with your English grammar.