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.
$3a + 4w < 49$ 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 nadias expectations by filtering air for 20 minutes and filtering water for 15 minutes?
choose 1 answer:
a the robot meets both of nadias expectations.
b the robot filters the expected amount of air and water, but it doesnt use the expected amount of energy.
c the robot uses the expected amount of energy, but it doesnt filter the expected amount of air and water.

Explanation:

Step1: Check the first inequality ($12A + 8W > 343$)

Substitute $A = 20$ and $W = 15$ into the left - hand side of the inequality $12A+8W$.
We know that $A = 20$ and $W = 15$, so $12\times20+8\times15=240 + 120=360$.
Since $360>343$, the robot meets the air - water filtering expectation.

Step2: Check the second inequality ($3A + 4W < 49$)

Substitute $A = 20$ and $W = 15$ into the left - hand side of the inequality $3A + 4W$.
We have $3\times20+4\times15 = 60+60 = 120$.
Since $120>49$, the robot does not meet the energy - usage expectation.

Answer:

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