Question

Or

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Kendra and Grace both went bowling last weekend, but not together. Kendra went during open bowling time, paying $1 for shoe rental and $5 per hour. Grace went on family night, when each hour was $2 and shoe rental was $16. As it turned out, they played for the same number of hours and spent the same amount. How much did each one spend? How many hours did each one bowl?


Kendra and Grace each spent $
and bowled for
hours.

Answer 1

Kendra and Grace each spent $26 and bowled for 5 hours. We set up a system of linear equations and solved it to find the number of hours they bowled and the total cost for each.

Step-by-step explanation:

To solve for the amount Kendra and Grace each spent and the number of hours they bowled, we need to set up a system of linear equations based on the given information. Let x represent the number of hours they bowled, and y represent the total cost.

For Kendra, the cost is calculated by a $1 shoe rental plus $5 per hour, resulting in the equation y = 1 + 5x. For Grace, the cost is a $16 shoe rental plus $2 per hour, resulting in the equation y = 16 + 2x.

Since they both spent the same amount and bowled for the same number of hours, we can equate the two equations:

• 1 + 5x = 16 + 2x

Isolate the variable x by subtracting 2x from both sides:

• 3x = 15

Divide both sides by 3 to solve for x:

• x = 5

They both bowled for 5 hours. Now we can plug this back into any of the equations to find the total cost:

• y = 1 + 5(5)
• y = 1 + 25
• y = 26

Kendra and Grace each spent $26 and bowled for 5 hours.