Question

Guests at the state park can rent paddle boats and kayaks. The rental cost in dollars, y, and the amount of time in hours, x, are represented by the equations shown: Paddle boat rental: y = 12x + 15, Kayak rental: y = 15x + 3. Enter the value of x to make the statement true: The cost of renting a paddle boat and the cost of renting a kayak are the same when rented for x hours.

Answer 1

The value of x that makes the cost of renting a paddle boat and the cost of renting a kayak the same is 4 hours.

Step-by-step explanation:

To find the value of x that makes the cost of renting a paddle boat and the cost of renting a kayak the same, we need to set the two equations equal to each other and solve for x. So, we have:

12x + 15 = 15x + 3

Subtracting 12x from both sides:

15 = 3x + 3

Subtracting 3 from both sides:

12 = 3x

Dividing both sides by 3:

x = 4

Therefore, the value of x that makes the statement true is 4 hours.