Question

bill is filling up a tank with water for some fish in a pet shop. he needs the tank to have at least 80 liters of water for the fish to survive in it, and at most 110 liters to avoid it being too full. the hose he is using fills the tank with 30 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. 2 ≤ x ≤ 3 (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: Set up the inequality

The tank already has 20 liters of water. Bill fills the tank with 30 liters of water each minute ($x$ minutes), and the tank needs to have at least 80 liters and at most a certain amount to avoid overflow. The inequality for the amount of water in the tank is $20 + 30x\geq80$.

Step2: Solve the inequality for the lower - bound

Subtract 20 from both sides of $20 + 30x\geq80$:
$30x\geq80 - 20$, so $30x\geq60$. Then divide both sides by 30: $x\geq2$.

Step3: Consider the non - given upper - bound situation (assuming no upper - bound for just getting the lower bound of time to reach the minimum water level)

The compound inequality for the possible number of minutes $x$ is $x\geq2$.

Answer:

$x\geq2$

For part (b), to graph $x\geq2$ on a number line:

• Draw a number line.
• Mark a closed circle at 2 (because $x$ can equal 2, indicated by $\geq$) and draw an arrow to the right to represent all the numbers greater than or equal to 2.