15. a pool can hold 850 gallons. it now has 598 gallons of water and is being filled at the rate shown. how…

15. 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

15. 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

Answer

Explanation:

Step1: Write the inequality

The pool currently has 598 gallons and is filling at a rate of 15.75 gallons per minute. 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)

Answer:

The inequality is (598 + 15.75m\leqslant850) and the solution is (m\leqslant16). To graph this on the number - line: draw a number - line. Put a closed circle at (m = 16) (because (m) can be equal to 16) and draw an arrow to the left (since (m) can be any value less than or equal to 16).