To determine which option is the better deal for swimming at the local swim center, we can calculate the total cost for both choices based on a variable number of days swimming.
Option 1: Pay per day
- Cost per day: $7
- Total cost for \( x \) days: \( 7x \)
Option 2: Enrollment fee plus daily pass
- Enrollment fee: $30
- Cost per day after enrollment: $4
- Total cost for \( x \) days: \( 30 + 4x \)
To find out when the second option becomes a better deal than the first, we can set up an inequality:
\[ 30 + 4x < 7x \]
Subtract \( 4x \) from both sides:
\[ 30 < 3x \]
Now, divide both sides by 3:
\[ 10 < x \] or \[ x > 10 \]
This means that if a swimmer plans to swim more than 10 days in the month, the second option (enrollment fee plus reduced daily rate) becomes the better deal.
For example:
-
If swimming for 9 days:
- Option 1: \( 7 \times 9 = 63 \)
- Option 2: \( 30 + 4 \times 9 = 30 + 36 = 66 \)
Here, Option 1 is cheaper.
-
If swimming for 11 days:
- Option 1: \( 7 \times 11 = 77 \)
- Option 2: \( 30 + 4 \times 11 = 30 + 44 = 74 \)
Here, Option 2 is cheaper.
In summary, for anyone planning to swim more than 10 days in the month, the enrollment fee with the lower daily rate is the better deal. If swimming 10 days or less, it’s cheaper to pay the daily fee without enrolling.