Question

Ashley wants to buy some tickets to the park online. There are two plans to choose from. The first plan is a

flat rate of $15.23 per ticket The second plan has a membership fee of $42, and a fee of $1.23 per ticket. Let
x be the number of tickets and C be the cost.
Plan 1: C = 15.23x Plan 2: C = 42 + 1.23x
a. When are the costs of the two plans equal to each other? Explain.
b. What is the y-intercept of the line for each equation? What does it mean in this context?
c. What is the constant rate of change for each relationship? What does it mean in this context?
d. For Plan 1, how many tickets are possible if the total cost is at most $100? Explain.

Answer 1

a. The costs of the two plans are equal to each other when C1 = C2, or when 15.23x = 42 + 1.23x. Solving for x in this equation, we find that x = $28. This means that for x = 28, the cost of the two plans will be equal to each other.

b. The y-intercept of the line for each equation represents the cost of the tickets when x = 0, or when there are no tickets purchased. For Plan 1, the y-intercept is 15.23 * 0 = $0, which means that if no tickets are purchased, the cost will be $0. For Plan 2, the y-intercept is 42 + 1.23 * 0 = $42, which means that if no tickets are purchased, the cost will be $42 (due to the membership fee).

c. The constant rate of change for each relationship is the slope of the line representing the equation. For Plan 1, the slope is 15.23, which means that for every additional ticket purchased, the cost will increase by $15.23. For Plan 2, the slope is 1.23, which means that for every additional ticket purchased, the cost will increase by $1.23.

d. For Plan 1, the maximum total cost that is possible is $100. This means that 100 / 15.23 = 6.57 tickets can be purchased. However, since the number of tickets must be a whole number, only 6 tickets can be purchased. This is because 6 * 15.23 = $91.38, which is the maximum number of tickets that can be purchased for a total cost of $100 or less.