Question

Course challenge You might need: Calculator Nadia built a robot to filter air and water efficiently. She expects the robot to filter more than 343 liters of air and water while using less than 49 Joules of energy. 12A + 8W > 343 represents the number of minutes the robot filters air A and water W to filter more than 343 liters of air and water. 3 A + 4W < 49 represents the number of minutes the robot filters air and water while using less than 49 Joules of energy. Does the robot meet both of Nadia's expectations by filtering air for 20 minutes and filtering water for 15 minutes? Choose 1 answer: А. The robot meets both of Nadia's expectations. The robot filters the expected amount of air and water, but it doesn't use the expected amount B

Answer 1

We have an equation that represents the number of minutes the robot filters air A and water W to filter more than 343 liters of air and water.

If the robots filter air for 20 minutes and water for 15 minutes, replacing A as 20 and W as 15, let us check if the equation is true or not. A = 20, B = 15

`\begin{gathered} 12A+8W=12\cdot20+8\cdot15 \\ 240+120=360 \end{gathered}`

Let's check if it is true or not,

`\begin{gathered} 12A+8W>343 \\ 360>343 \end{gathered}`

TRUE, 360 is greater than 343.

This means the robot meets the first expectation.

We need to check the second equation, which represents the number of minutes the robot takes to filter air A and water W using less than 49 Joules. 3A + 4W < 49

We plug in the values we have for A and W, to check if the equation is true.

`\begin{gathered} 3A+4W=3\cdot20+4\cdot15 \\ 60+60=120 \end{gathered}`

Let's check if it is true or not,

`\begin{gathered} 3A+4W<49 \\ 120<49 \end{gathered}`

FALSE, 120 is greater than 49.

This means the robot does not meet the second expectation.

Answer: B. The robot filters the expected amount of air and water, but it doesn't use the expected amount of energy.