Question

tammy is filling up a tank with water for some fish in a pet shop. she needs the tank to have more than 85 liters of water for the fish to survive in it, and less than 145 liters to avoid it being too full. the hose she is using fills the tank with 30 liters of water each minute. the tank already has 25 liters of water in it. let x be the number of minutes she will continue to fill the tank.
(a) find the possible numbers of minutes she 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 she will continue to fill the tank.

Explanation:

Step1: Set up lower bound inequality

The total water is initial 25L plus 30L per minute, which must exceed 85L:
$25 + 30x > 85$

Step2: Solve lower bound for x

Subtract 25, then divide by 30:
$30x > 85 - 25$
$30x > 60$
$x > 2$

Step3: Set up upper bound inequality

Total water must be less than 145L:
$25 + 30x < 145$

Step4: Solve upper bound for x

Subtract 25, then divide by 30:
$30x < 145 - 25$
$30x < 120$
$x < 4$

Step5: Combine into compound inequality

Combine the two solved inequalities:
$2 < x < 4$

Step6: Graph the solution on number line

• Draw an open circle at $x=2$ (since $x>2$, not equal) and an open circle at $x=4$ (since $x<4$, not equal).
• Shade the segment of the number line between the two open circles.

Answer:

(a) $2 < x < 4$
(b) On the number line:

• Place an open circle at 2, an open circle at 4.
• Shade the region between 2 and 4.