Question

1. 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. then graph the solutions. filling rate of 15.75 gallons per minute

Explanation:

Step1: Write the inequality

The amount of water already in the pool is \(598\) gallons. The rate of filling is \(15.75\) gallons per minute. So the total amount of water after \(m\) minutes is \(598 + 15.75m\). Since the pool can hold at most \(850\) gallons, the inequality is \(598+15.75m\leq850\).

Step2: Solve the inequality for \(m\)

Subtract \(598\) from both sides:
\(15.75m\leq850 - 598\)
\(15.75m\leq252\)
Divide both sides by \(15.75\):
\(m\leq\frac{252}{15.75}\)
\(m\leq16\)

Answer:

The inequality is \(598 + 15.75m\leq850\) and the solution is \(m\leq16\). On the number - line, we draw a closed circle at \(16\) (because \(m = 16\) is included in the solution set) and shade to the left of \(16\).