Question

A group spends $277.50 to rent a total of 15 tubes. How many of each type of tube does the group rent? ( 1 person tube is $12.50 & 2 person tube is $20)

Answer 1

The group rents 3 one-person tubes at $12.50 each and 12 two-person tubes at $20 each. This conclusion is reached by setting up a system of linear equations based on the total cost and the number of tubes, and solving for the variables representing the quantities of each type of tube.

Step-by-step explanation:

To solve the problem, we can set up a system of linear equations to determine how many of each type of tube the group rents. Let's denote x as the number of 1-person tubes at $12.50 each, and y as the number of 2-person tubes at $20 each.

The total cost for the tubes is $277.50, and the total number of tubes rented is 15. We can set up the following equations:

1. 12.50x + 20y = 277.50 (total cost equation)
2. x + y = 15 (total number of tubes)

We can solve these equations using either substitution or elimination. Here's how you could solve using substitution:

1. From the second equation, we solve for y: y = 15 - x.
2. Substitute y into the first equation: 12.50x + 20(15 - x) = 277.50.
3. Simplify and solve for x:

• 12.50x + 300 - 20x = 277.50
• -7.50x + 300 = 277.50
• -7.50x = -22.50
• x = 3 (number of 1-person tubes)

Substitute x back into the equation y = 15 - x to find y:

• y = 15 - 3
• y = 12 (number of 2-person tubes)

Therefore, the group rents 3 one-person tubes and 12 two-person tubes.