Question

Alice’s Athletic Arena requires members to pay $20 to join and members must pay $1.50 for each time they come to work out. Roy’s Romper Room requires members to pay $5 to join and members must pay $4 for each time they come to work out. How many visits will it take for the costs to both be the same?

Answer 1

Answer:

6 visits will it take for the costs to be the same

Step-by-step explanation:

The form of the linear relation is y = m x + b, where

• m is the rate of change

• b is the initial amount

Assume that the number of visits is x, and the total cost is y

∵ Alice’s Athletic Arena requires members to pay $20 to join

→ That means there is an initial amount of $20

∴ b = 20

∵ The members must pay $1.50 for each time they come to work out

→ That means there is a cost for every visit (rate of change)

∴ m = 1.5 dollars/visit

∵ The number of visits = x

∵ The total cost is y

→ Form the linear equation for this situation

∴ y = 1.5x + 20 ⇒ (1)

∵ Roy’s Romper Room requires members to pay $5 to join

∴ b = 5

∵ The members must pay $4 for each time they come to work out

∴ m = 4 dollar/visit

→ Form the linear equation for this situation

∴ y = 4x + 5 ⇒ (2)

∵ The costs to both are the same

→ That means, equate the right sides of (1) and (2)

∴ 1.5x + 20 = 4x + 5

→ Subtract 20 from both sides

∴ 1.5x + 20 - 20 = 4x + 5 - 20

∴ 1.5x = 4x - 15

→ Subtract 4x from both sides

∵ 1.5x - 4x = 4x - 4x - 15

∴ -2.5x = -15

→ Divide both sides by -2.5

∴ x = 6

∴ 6 visits will it take for the costs to be the same