Question

For an experiment, the temperature of a liquid must stay above 60°F . The starting temperature of the liquid is 90°F . It is placed in a cooler, which lowers its temperature 3°F each minute.
Let m represent the number of minutes the liquid is in the cooler.
Which statement determines how many minutes the liquid can stay in the cooler?
The liquid must be in the cooler fewer than 10 minutes.
The liquid must be in the cooler fewer than 15 minutes.
The liquid must be in the cooler fewer than 30 minutes.
The liquid must be in the cooler fewer than 60 minutes.

Answer 1

The answer is The liquid must be in the cooler fewer than 10 minutes.

Let:
m - the number of minutes the liquid is in the cooler.
a - the starting temperature
The function is:
f(m) = a - 3 * m     (Since the temperature decreases by 3°F each minute m, it has a negative sign)
Let:
m - the number of minutes the liquid is in the cooler.
a - the starting temperature
a = 90°F 

The temperature of a liquid must stay above 60°F:
f(m) > 60

Thus:
f(m) = a - 3 * m 
f(m) > 60

a - 3 * m > 60
90 - 3m > 60
90 - 60 > 3m
30 > 3 m
30/3 > m
10 > m
Or m < 10. So the correct answer is The liquid must be in the cooler fewer than 10 minutes.