Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. ariana and judith both went bowling last weekend, but not together. ariana went during open bowling time, paying $15 for shoe rental and $1 per hour. judith went on family night, when each hour was $5 and shoe rental was $3. 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? ariana and judith each spent $\underline{\quad}$ and bowled for $\underline{\quad}$ hours.

Explanation:

Step1: Define variables

Let $h$ = number of hours bowled, $C$ = total cost.

Step2: Set up Ariana's cost equation

Ariana's cost: fixed rental + hourly rate.
$C = 15 + 1h$

Step3: Set up Judith's cost equation

Judith's cost: fixed rental + hourly rate.
$C = 3 + 5h$

Step4: Substitute equal costs

Set equations equal (same total cost).
$15 + h = 3 + 5h$

Step5: Solve for $h$

Isolate $h$ terms and calculate.
$15 - 3 = 5h - h$
$12 = 4h$
$h = \frac{12}{4} = 3$

Step6: Find total cost $C$

Substitute $h=3$ into Ariana's equation.
$C = 15 + 1(3) = 18$

Answer:

Ariana and Judith each spent $\$18$ and bowled for $3$ hours.