September 2010
Problem of the Month

Humidifier Problem

On MR. P's humidifier, it states that

When the outside temperature is -20 degrees, you should set the humidifier at 15%;

When the outside temperature is 0 degrees, you should set the humidifier at 25%;

When the outside temperature is 20 degrees, you should set the humidifier at 35%;


(1) What should Mr. P set the humidifier at when the outside temperature is 7 degrees?

(2) Determine the equation that relates the Humidifier setting H to the outside temperature T.

(3) The highest setting on Mr. P's Humidifier is 45%.   At what outside temperature should he use this setting?

Solution to the Problem:

The answers are:
(1) 28.5%
(2) H = T / 2 + 25
(3) T = 40 degrees.

First solve for the general equation relating H to T.

Consider the three sets of ordered pairs (T, H): (-20, 15), (0, 25), (20, 35).

These three coordinates fall on a line since the slope is the same between any two points.

The slope is 1/2.

The second ordered pair gives the y-intercept (when T = 0, H = 25).

Therefore the equation is H = 1/2 T + 25.

Now use the equation to solve for parts (1) and (3).

(1) H = 7/2 + 25 = 28.5%.
(3) 45 = T / 2 + 25, so T = 40.

Correctly solved by:

1. John C. Funk	Ventura, California
2. Judi Breault	Tucson, Arizona
3. David & Judy Dixon	Bennettsville, South Carolina
4. Dylan Martin	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher