Question

Alvira wants to use the community pool. She's trying to decide which plan she should choose. "Pay As You Go" Plan charges $7 per visit, the Value Plan has a $24 annual fee and charges $3 per visit, and the Divers Plan has a $35 annual fee and charges $2 per visit.

a. Represent each community pool plan with a rule (3 rules).

b. How many visits would be needed for the cost to be the same for "Pay As You Go" and Value Plans? What about Value and Divers Plans?

c. If Alvira will probably only visit the pool a few times a year, which plan
should she choose? Why?

Answer 1

Explanation:

a. Let x represent the amount of times Alvira uses the community pool.

Pay As You Go Plan: 7x

Value Plan: 3x+24

Divers Plan: 2x+35

b.

Method 1: Solve algebraically

Set the Pay As You Go Plan equal to the Value Plan and solve for x. We do this as you x represents the amount of visits, and you want to find the amount of visits needed for the two of them to be equal.

`7x=3x+24\\4x=24\\x=6`

Alvira would need to go 6 times for the cost to be the same for the Pay As You Go and the Value Plans.

Set the Pay As You Go Plan equal to the Divers Plan and solve for x to find the amount of visits needed for the cost to be the same for these two plans.

`7x=2x+35\\5x=35\\x=7`

Alvira would need to go 7 times for the cost to be the same for the Pay As You Go and the Value Plans.

Method 2: Graph

You can hand graph, graph from a calculator, or visit a graphing website such as Desmos.

Have the equations y=7x, y=3x+24, and y=2x+35. See where y=7x intersects y=3x+24 and then find where it intersects y=2x+35. You should find that the answers will be the same as Method 1, 6 times and 7 times, respectively

.

c. If Alvira will only visit the pool a few times a year, she should choose the Pay As You Go Plan. If she goes less than 6 times, then she should use this plan as it is the cheapest and therefore can save money.

Answer 2

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Explanation:

u many visits would be needed for the cost to be the same for "Pay As You Go" and Value Plans? What about Value and Divers Plans?

c. If Alvira will probably only visit the pool a few times a year, which plan

should she choose? Why?