Answer:
6 visits will it take for the costs to be the same
Explanation:
The form of the linear relation is y = m x + b, where
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