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: Set up the inequality

The pool currently has 598 gallons. Water is filling at a rate of 15.75 gallons per minute (\(m\) minutes). The pool can hold at most 850 gallons. So the inequality is \(598 + 15.75m\leqslant850\).

Step2: Solve the inequality for \(m\)

Subtract 598 from both sides:
\(15.75m\leqslant850 - 598\)
\(15.75m\leqslant252\)
Divide both sides by 15.75:
\(m\leqslant\frac{252}{15.75}\)
\(m\leqslant16\)

Step3: Graph the solution

On the number - line, we draw a closed circle at 16 (because \(m = 16\) is included in the solution, since when \(m = 16\), \(598+15.75\times16=598 + 252=850\)) and shade to the left of 16.

Answer:

The inequality is \(598 + 15.75m\leqslant850\) and the solution is \(m\leqslant16\). On the number - line, a closed circle at 16 and shading to the left.