Question

hong is filling up a tank with water for some fish in a pet shop. he needs the tank to have more than 95 liters of water for the fish to survive in it, and less than 170 liters to avoid it being too full. the hose he is using fills the tank with 25 liters of water each minute. the tank already has 20 liters of water in it. let x be the number of minutes he will continue to fill the tank. (a) find the possible numbers of minutes he will continue to fill the tank. write your answer as a compound inequality solved for x. (b) on the number line below, graph the solution that represents the possible numbers of minutes he will continue to fill the tank.

Explanation:

Step1: Define total water equation

Total water: $20 + 25x$

Step2: Set lower inequality

Solve for minimum $x$:
$20 + 25x > 95$
$25x > 95 - 20$
$25x > 75$
$x > \frac{75}{25}$
$x > 3$

Step3: Set upper inequality

Solve for maximum $x$:
$20 + 25x < 170$
$25x < 170 - 20$
$25x < 150$
$x < \frac{150}{25}$
$x < 6$

Step4: Combine into compound inequality

Combine the two results.

Answer:

(a):
$3 < x < 6$