Question

Jordan uses a prepaid card to buy movie tickets. The initial value of the card is $240, and each movie ticket costs $15. Let m(x) represent the amount of money, m, in dollars that remains on the card after purchasing x movie tickets.(6 points) Part C: The constraints are: 0 ≤ x ≤ 16 and ?

Answer 1

To express the constraints for the function \( m(x) \), we need to understand how many movie tickets Jordan can purchase with the initial amount on the prepaid card and how that affects the remaining balance.

Given:
- The initial value of the prepaid card is $240.
- Each movie ticket costs $15.

The function \( m(x) \) is defined as:
\[
m(x) = 240 - 15x
\]

### Constraints:
1. **Non-Negative Tickets**: Jordan cannot purchase a negative number of tickets, which gives us the constraint:
\[
x \geq 0
\]

2. **Maximum Tickets Based on Card Value**: To find the maximum number of tickets Jordan can buy with his $240, we set up the inequality:
\[
240 \geq 15x
\]
Dividing both sides by 15:
\[
16 \geq x \quad \text{or} \quad x \leq 16
\]

### Combined Constraints:
Putting these together, the constraints for \( x \) are:
\[
0 \leq x \leq 16
\]

Thus, the complete answer for the constraints is:
- \( 0 \leq x \leq 16 \)

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