To rent a jet ski at Sam's costs $25 plus $3 per hour. At Claire's, it costs $7 plus $6 per hour. At how many hours will the rental cost at both shops be equal?

The number of hours that the cost of renting a ski jet will become equal in both shops is 6 (hours)

Step-by-step explanation:

Extracting the key information from the question:-

** * Renting a jet ski at Sam's establishment costs $25 and additional $3 per hour.

** * Again, it costs $7 and additional $6 per hour to rent a jet ski at Claire's establishment.

** * We are required to find out the number of hours that the rental cost of jet ski at both shops will be the same.

What we are basically required to do is to find that number of hours that you can rent a jet ski and you wouldn't need to worry about the shop that renting it's jet ski will be more affordable in because the cost will be the same in both establishment when renting the jet ski at a particular number of hours.

For example, in that number of hours, the cost in Sam's shop and Claire's shop will now both be say, $50.

Since it costs a down payment of $25 plus additional $3 for each hour we make use of the jet ski at Sam's establishment, then the cost of renting a jet ski at Sam's shop for that number of hours that the cost will become equal in both shops is:

= 25 + 3x

Again, we are informed that it costs $7 down payment and additional $6 per hour that a jet ski from Claire's establishment will b rented and used. Then the cost of renting a jet ski at Claire's establishment for that number of hours that the cost will become equal in both shops is:

= 7 + 6x

Since at this unknown number of hours (x hours) the cost of renting a jet ski at Sam's shop will be equal to the cost of renting a jet ski at Claire's establishment, then marrying the equations, we will have:-

25 + 3x = 7 + 6x

We now pair like terms

6x - 3x = 25 - 7

3x = 18

x = 18/3

x = 6

Therefore, that number of hours that the cost of renting a jet ski will become equal in both Sam's and Claire's establishment is 6 hours.