Question

A town pool has two individual membership rates. You can pay a $75 membership fee and then $2 each time you use the pool or you can pay a $15 membership fee and $5 each time you use the pool. Write and solve an equation to determine how many times you must visit the pool for the costs to be equal.

Answer 1

20

Explanation:

Let the number of times to visit the pool be x

Then there are 75+2x=15+5x

Solve for x=20

So the cost is equal when visiting the pool 20 times

Answer 2

20 times

Explanation:

Let's form two expressions relating the amount you would pay in each scenario:

• If we consider
`x` to be the number of times you use the pool, and you pay $2 each time with a $75 membership fee, then

total cost =
`\boxed{2x + 75}`

• If you pay $5 each time with a $15 membership fee, then

total cost =
`\boxed{5x + 15}`

According to the question, the two costs should be equal.

∴
`2x + 75 = 5x + 15`

Now we have to solve for
`x`:

⇒
`75 = 5x+ 15 - 2x` [subtracting
`2x` from each side]

⇒
`75 = 15 + 3x`

⇒
`60 = 3x` [subtract 15 from each side]

⇒
`20 = x`

∴
`x = \bf 20`

This means that you must visit the pool 20 times for the costs to be equal.