Question

Solve using a system of equations. Lucia wants to go ice skating. She must pay for admission and then rent ice-skates. Rates for two rinks near her home are shown below.

Ice Plex
$5 for Admission plus $2 per hour of skate rental

Skate World
$10 for admission plus $1 per hour for skate rental

Let x represent the cost of admission in dollars and let y represent the number of hours skates are rented for. Write a system of equations to represent the problem.

Please help! I cannot figure this out

Answer 1

We represent the total cost of going ice skating with 'x' for the cost and 'y' for the hours of skate rental. For Ice Plex, the equation is x = 5 + 2y, and for Skate World, it is x = 10 + y. These two equations form a system to solve for the cost comparisons.

Step-by-step explanation:

To solve Lucia's ice skating costs using a system of equations, we need to express the total cost of going to each ice rink as an equation. We are told that for Ice Plex, the admission is $5 and the skate rental is $2 per hour. For Skate World, the admission is $10 and the skate rental is $1 per hour. We can use x to represent the total cost of going skating and y to represent the number of hours she rents the skates.

Therefore, the equations for the two rinks are:

• Ice Plex: x = 5 + 2y
• Skate World: x = 10 + y

These equations form our system of equations that can be solved to find out the number of hours she needs to skate for the costs at both rinks to be equal, or to determine which rink is more cost-effective based on the number of hours she plans to skate.

Answer 2

Ice Plex - Y = 2x+5 Skate World- Y = 10x+1