Question

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. 3A+4W < 49presents 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?

Answer 1

The robot filters the expected amount of air and water, but it doesn’t use the expected amount of energy

Answer 2

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.

If the robot filters air for 20 minutes and water for 15 minutes, plugging A as 20 and W as 15, let us check if the equation is true or not.

Checking left side:

12A + 8W = 12(20) +8(15)

240+ 120 = 360

Checking right side: 343

12A+8W > 343

360>343

True.

So the robot meets the first expectation.

Let us check for second equation:

3A+4W < 49

Left side : 3A +4W = 3(20) +4(15) = 60 +60 =120

Right side is 49

comparing left and right side:

3A+4W < 49

120<49

False.

So the robot does not meet the second expectation.