Question

I can't fail 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

The costs will be equal after visiting the pool 15 times.

Step-by-step explanation:

To determine when the costs are equal for both membership options, we can set up an equation. Let
`\( x \)`represent the number of times the pool is visited.

For the first option, the cost is
`\( 75 + 2x \)`, and for the second option, the cost is
`\( 15 + 5x \)`. Setting these two expressions equal to each other gives us the equation:

`\[ 75 + 2x = 15 + 5x \]`

To solve for
`\( x \)`, we can first simplify the equation by subtracting 15 from both sides:

`\[ 60 + 2x = 5x \]`

Next, subtracting
`\( 2x \)` from both sides gives:

`\[ 60 = 3x \]`

Finally, dividing both sides by 3:

`\[ x = 20 \]`

So, the costs will be equal after visiting the pool 20 times. It's important to note that the number of visits must be a whole number, so we round down to the nearest whole number since you can't visit the pool a fractional number of times.

In conclusion, after 20 visits, the total cost for both membership options will be the same, amounting to $135.

This solution ensures that neither option is more economical than the other over time, providing a clear understanding of the break-even point for the two membership rates.