A robot is expected to filter pollution out of at least $350$ liters of air and water. It filters air at the rate of $50$ liters per minute, and it filters water at the rate of $20$ liters per minute. Which of the following inequalities represents the number of minutes the robot should filter air $(A)$ and water $(W)$ to meet this expectation? $\newline$ Choose $1$ answer: $\newline$ (A) $50A+20W \geq 350$ $\newline$ (B) $50A+20W \leq 350$ $\newline$ (C) $20A+50W \geq 350$ $\newline$ (D) $20A+50W \leq 350$

Full solution

Q. A robot is expected to filter pollution out of at least

350

liters of air and water. It filters air at the rate of

50

liters per minute, and it filters water at the rate of

20

liters per minute. Which of the following inequalities represents the number of minutes the robot should filter air

(A)

and water

(W)

to meet this expectation?

\newline

Choose

1

answer:

\newline

(A)

50A+20W \geq 350

\newline

(B)

50A+20W \leq 350

\newline

(C)

20A+50W \geq 350

\newline

(D)

20A+50W \leq 350

Understand the problem: Understand the problem. $\newline$ The robot filters air and water at different rates, and we want to find an inequality that represents the condition for the robot to filter at least $350$ liters of air and water combined.
Set up the inequality: Set up the inequality based on the given rates. $\newline$ The robot filters air at a rate of $50$ liters per minute, which we can represent as $50A$ , where $A$ is the number of minutes spent filtering air. It filters water at a rate of $20$ liters per minute, which we can represent as $20W$ , where $W$ is the number of minutes spent filtering water. Since the robot needs to filter at least $350$ liters, we use the 'greater than or equal to' sign ( $\geq$ ).
Write the inequality: Write the inequality. $\newline$ Combining the rates for air and water, we get the inequality $50A + 20W \geq 350$ . This inequality represents the condition that the total volume of air and water filtered should be at least $350$ liters.
Check the answer choices: Check the answer choices to find the matching inequality. $\newline$ Looking at the answer choices, we see that option (A) matches the inequality we derived: $50A + 20W \geq 350$ .