Question

keisha is filling up a tank with water for some fish in a pet shop. she needs the tank to have more than 130 liters of water for the fish to survive in it, and less than 230 liters to avoid it being too full. the hose she is using fills the tank with 25 liters of water each minute. the tank already has 30 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.

Explanation:

Step1: Define total water expression

Total water: $30 + 25x$

Step2: Set lower bound inequality

$30 + 25x > 130$
Subtract 30: $25x > 100$
Divide by 25: $x > 4$

Step3: Set upper bound inequality

$30 + 25x < 230$
Subtract 30: $25x < 200$
Divide by 25: $x < 8$

Step4: Combine inequalities

Merge the two results.

Answer:

$4 < x < 8$