Question

A tank can hold a maximum of 400 gallons of water. The volume of water when pumping water into the tank can be determined by the function f (m) = 12.5m + 25 where m is the number of minutes that the pump is running and f(m) is the volume of gallons of water in the tank. If the tank must maintain a minimum of 25 gallons of water, which inequality represents the domain of this situation?
(Hint: The variable f(m) is like "y" and m is like "x")
0 < m < 400
30 < m < 400
25 < m < 400
0 < m < 30

Answer 1

Inequalities help us to compare two unequal expressions. The inequality that represents the domain of this situation is 0<m<30.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that the volume of the tank should be between 400 gallons of water to 25 gallons of water. While the function of the volume of the water is given as,

f(m) = 12.5m + 25,

Now to know the value of m for which the volume of water in the tank is 400 gallons.

$f(m) = 12.5m + 25\\\\400=12.5+25\\\\375=12.5m\\\\m = 30$

Also, the value of m for which the volume of the water in the tank is 25 gallons is,

$f(m) = 12.5m + 25\\\\25=12.5+25\\\\0=12.5m\\\\m = 0$

Hence, the inequality that represents the domain of this situation is 0<m<30.

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