4. A pool can hold 850 gallons. It now has 598 gallons of water and is being filled at the rate shown. How many more minutes, \( m \), can water continue to flow into the pool before it overflows? Write and solve an inequality.

To solve the problem, we need to determine how many more minutes, \( m \), water can flow into the pool before it overflows. ### Known Conditions: 1. The total capacity of the pool is 850 gallons. 2. The current amount of water in the pool is 598 gallons. 3. The rate at which water is being filled is not specified in the problem statement, so we will denote it as \( r \) gallons per minute. ### Step 1: Set up the inequality The amount of water that can still be added to the pool before it overflows is given by the difference between the total capacity and the current amount of water: \[ 850 - 598 = 252 \text{ gallons} \] The amount of water added over \( m \) minutes at a rate of \( r \) gallons per minute is \( r \cdot m \). To prevent overflow, the total amount of water in the pool after \( m \) minutes must be less than or equal to the pool's capacity: \[ 598 + r \cdot m \leq 850 \] ### Step 2: Rearranging the inequality Now, we can rearrange the inequality to isolate \( m \): \[ r \cdot m \leq 850 - 598 \] \[ r \cdot m \leq 252 \] \[ m \leq \frac{252}{r} \] ### Conclusion The inequality \( m \leq \frac{252}{r} \) tells us how many more minutes water can flow into the pool before it overflows, depending on the rate \( r \). If you provide the rate \( r \), we can calculate the exact number of minutes \( m \).