Question

A hot liquid is placed in a freezer to cool it down faster. The temperature of the liquid, in degrees Fahrenheit, is given by the expression 144-8m where m is the number of minutes it has been in the freezer. The cook wants to remove the liquid from the freezer when its temperature is at most 50°F. Which inequality below represent all amounts of times that the liquid can stay in the freezer?

(1) m>14.25
(2) m≥ 11.75
(3) m<11.75
(4) m≤ 14.25

Answer 1

To find the maximum time the liquid can stay in the freezer before reaching 50°F, we solve the inequality 144 - 8m ≤ 50, which simplifies to m ≤ 11.75. This represents all amounts of time that the liquid can stay in the freezer.

Step-by-step explanation:

The question asks to determine the inequality that represents all possible amounts of time the liquid can stay in the freezer given the expression for its temperature over time, 144-8m, where m is the number of minutes. The cook wants the temperature to be at most 50°F. We set up the inequality as follows:

144 - 8m ≤ 50

We solve for m:

144 - 50 ≤ 8m

94 ≤ 8m

Divide both sides by 8:

m ≤ 11.75

Thus, the correct inequality representing the time the liquid can stay in the freezer is m ≤ 11.75, which corresponds to inequality (3).