Question

charmaine is pumping water into an aquarium at a rate of 13 liters per minute. the aquarium had 25 liters of water in it before she started. her goal is given by 13x + 25 ≤ 298, where x is the number of minutes she pumps water into the aquarium. complete the parts below. (a) solve the given inequality and graph the solution on the number line below. (b) choose and complete the statement that best describes the solution. ○ to meet the goal, the aquarium will have at least liters of water in it. this will take at most minutes. ○ to meet the goal, the aquarium will have at most liters of water in it. this will take at most minutes. ○ to meet the goal, the aquarium will have at most liters of water in it. this will take at least minutes.

Explanation:

Step1: Solve the inequality

Given \(13x + 25\leq288\).
Subtract 25 from both sides: \(13x\leq288 - 25\), so \(13x\leq263\).
Divide both sides by 13: \(x\leq\frac{263}{13}\approx20.23\).

Step2: Analyze the number of liters

The amount of water in the aquarium is \(13x + 25\). Since \(x\leq20.23\), the amount of water \(13x+25\leq288\) (the goal). The time \(x\) is non - negative (\(x\geq0\)). The number of liters of water \(y = 13x + 25\). When \(x = 0\), \(y = 25\) (initial amount). As \(x\) increases up to approximately \(20.23\), \(y\) increases up to 288. So, to meet the goal, the aquarium will have at most 288 liters of water and it will take at most approximately 20.23 minutes.

Answer:

(a) The solution of the inequality \(13x + 25\leq288\) is \(x\leq\frac{263}{13}\approx20.23\). On the number - line, we draw a closed circle at \(x = 0\) (since \(x\) represents time and \(x\geq0\)) and a closed circle at \(x\approx20.23\) (because the inequality is \(\leq\)) and shade the line between them.
(b) To meet the goal, the aquarium will have at most 288 liters of water. This will take at most approximately 20.23 minutes.