Question

61. A city park is opening a new swimming pool. You can pay a daily entrance fee of $3 or purchase a membership for the 12-week summer season for $82 and pay only $1 per day to swim. How many days would you have to swim to make the membership worthwhile?

Answer 1

I don't have anything for this one yet, just a bunch of numbers all over the place. ^^;

Answer 2

Let a variable, like x, equal the number of days.
Write an expression for each way of paying using x.
Set the expressions equal and solve for x.

Answer 3

Start by using x = number of days.

!st payment method: You can pay a daily entrance fee of $3

If you pay $3 per day for x number of days, how much do you pay?

Answer 4

That one's just 3x!

Answer 5

Good.
Now the 2nd payment method.
"purchase a membership for the 12-week summer season for $82 and pay only $1 per day"

Answer 6

Is the other one 82 + 84? There are 84 days in 12 weeks, so,

Answer 7

No.
The 2nd method has a fixed $82, so your 82 is correct.
Then you pay an additional $1 per day for x days.

Answer 8

Ah, so just 82+x? Since 1x = x

Answer 9

Exactly.
Now set the 2 expressions equal and solve for x.

Answer 10

3x = 82 + x

Did you solve for x?

Answer 11

It's 2x = 82, which then becomes x = 41!

Answer 12

So you would have to swim 41 days to make your membership worth your money.

Answer 13

Correct.
That means it takes 41 days of swimming to make the two payment methods equal.
You are correct.
If you swim ecactly 41 days, you come out even.
If you swim more then 41 days, then the $82 membership is worthwhile.

Answer 14

Thank you, once again, for your help!

Answer 15

You're welcome.