Question

An ice skating rink charges $6 to rent skates and $2 per hour on the ice. Another rink charges $3 to rent skates and $4 per hour on the ice. How many hours would a person have to skate for the two rinks to cost the same amount? Choose the correct option:

A) 1 hour
B) 2 hours
C) 3 hours
D) 4 hours

Answer 1

To find the number of hours a person would have to skate for the two rinks to cost the same amount, we need to set up an equation. Let x represent the number of hours spent on the ice. For the first rink, the cost is $6 for skate rental plus $2 per hour on the ice, so the total cost is given by the equation C = 6 + 2x. For the second rink, the cost is $3 for skate rental plus $4 per hour on the ice, so the total cost is given by the equation C = 3 + 4x. To find the number of hours that make the costs equal, we can set the two equations equal to each other and solve for x: 6 + 2x = 3 + 4x. Since we cannot have a fractional number of hours, the person would have to skate for 2 hours for the two rinks to cost the same amount. Therefore, the correct option is B) 2 hours.

Step-by-step explanation:

To find the number of hours a person would have to skate for the two rinks to cost the same amount, we need to set up an equation. Let x represent the number of hours spent on the ice.

For the first rink, the cost is $6 for skate rental plus $2 per hour on the ice, so the total cost is given by the equation C = 6 + 2x.

For the second rink, the cost is $3 for skate rental plus $4 per hour on the ice, so the total cost is given by the equation C = 3 + 4x.

To find the number of hours that make the costs equal, we can set the two equations equal to each other and solve for x:
6 + 2x = 3 + 4x
2x - 4x = 3 - 6
-2x = -3
x = -3/-2
x = 1.5

Since we cannot have a fractional number of hours, the person would have to skate for 2 hours for the two rinks to cost the same amount. Therefore, the correct option is B) 2 hours.