Gabby and Brenda both went bowling last weekend, but not together. Gabby went during open bowling time, paying $7 for shoe rental and $1 per hour. Brenda went on family night, when each hour was $3 and shoe rental was $3. As it turned out, they played for the same number of hours and spent the same amount. How many hours did each one bowl?

Question

Let x represent the number of hours and y represnt the amount spent.

2 hours

4 hours

6 hours

8 hours

Answer 1

Let's set up a system of equations to represent the information given in the problem:

For Gabby:
y = 7 + x (she paid $7 for shoe rental and $1 per hour)

For Brenda:
y = 3x + 3 (she paid $3 per hour and $3 for shoe rental)

Since they played for the same number of hours and spent the same amount, we can set the two expressions for y equal to each other:

7 + x = 3x + 3

Subtracting 3x from both sides, we get:

7 + x - 3x = 3

-2x + x = -4

Simplifying,

-x = -4

Dividing both sides by -1, we find:

x = 4

So they both played for 4 hours.