Question

Two families go ice-skating one day. One family spends $15 for skate rentals and pays five dollars per hour to skate. The second family spends $25 for skate rentals and pays three dollars per hour to skate. How long can they skate before both of the places cost the same?

Answer 1

To find out how long two families can ice-skate before the costs are the same, we set up two cost equations and solve for the number of hours. After doing the math, we find that both families will have the same costs after ice-skating for 5 hours.

Step-by-step explanation:

The question asks us to determine how long two families can ice-skate before both accumulate the same costs. We set up two equations representing the total cost for each family. Let 'x' represent the number of hours they skate.

• Family 1: Total Cost = $15 (flat rate) + $5 (per hour) × x
• Family 2: Total Cost = $25 (flat rate) + $3 (per hour) × x

To find when the costs will be the same, we set the two equations equal to each other:

$15 + $5x = $25 + $3x

Solving for 'x', we subtract $3x from both sides:

$2x = $10

Dividing both sides by $2:

x = 5

Therefore, both families will have the same costs after ice-skating for 5 hours.