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Fernando built a robot to filter air and water efficiently. He expects the robot to filter more than $512$ liters of air and water while using less than $9$ Joules of energy. $\newline$ $A$ represents the number of minutes the robot filters air, and $\newline$ $W$ represents the number of minutes the robot filters water. $\newline$ 21A + 14W > 512 represents the number of minutes the robot filters air and water to filter more than $512$ liters of air and water. $\newline$ 0.36A + 0.6W < 9 represents the number of minutes the robot filters air and water while using less than $9$ Joules of energy. $\newline$ Does the robot meet both of Fernando's expectations by filtering air for $15$ minutes and filtering water for $5$ minutes?

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Evaluate two-variable equations: word problems

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Q. Fernando built a robot to filter air and water efficiently. He expects the robot to filter more than

512

liters of air and water while using less than

9

Joules of energy.

\newline

A

represents the number of minutes the robot filters air, and

\newline

W

represents the number of minutes the robot filters water.

\newline

21A + 14W > 512

represents the number of minutes the robot filters air and water to filter more than

512

liters of air and water.

\newline

0.36A + 0.6W < 9

represents the number of minutes the robot filters air and water while using less than

9

Joules of energy.

\newline

Does the robot meet both of Fernando's expectations by filtering air for

15

minutes and filtering water for

5

minutes?

Calculate Total Liters: Calculate the total liters of air and water filtered using the equation $21A + 14W$ . Calculation: $21(15) + 14(5) = 315 + 70 = 385$ liters.
Check Total Liters: Check if the total liters filtered is more than $512$ liters. $\newline$ Comparison: 385 > 512? No.
Calculate Total Energy: Calculate the total energy used using the equation $0.36A + 0.6W$ . Calculation: $0.36(15) + 0.6(5) = 5.4 + 3 = 8.4$ Joules.
Check Total Energy: Check if the total energy used is less than $9$ Joules. $\newline$ Comparison: 8.4 < 9? Yes.

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