Algebra III
3.7 - Direct and Inverse Variation Word Problems
1.
The number of pounds you weigh is directly proportional to the number of kilograms you are. Kay Dense steps
onto a scale calibrated in kilograms and finds that she is 50 kilograms. She knows that she weighs 110 pounds.
a.
Write the particular equation expressing pounds in terms of kilograms.
b.
How many pounds would a person weigh if the scale read:
c.
2.
Name _______________________________
i.
100 kilograms?
ii.
25 kilograms?
iii.
150 kilograms?
How many kilograms would Stan be if he weighed 165 pounds?
The number of houses that can be served by a water main is directly proportional to the square of the diameter
of the main. This is because the cross sectional area of the pipe, and thus the number of liters per minute that
can flow, varies directly with the square of the diameter. Suppose that the City Waterworks has 10 cm diameter
water main that can supply 50 houses.
a.
Write the particular equation for this function.
b.
How many houses could be served by a water main of diameter:
c.
i.
30 cm?
ii.
43 cm?
iii.
1 meter (how many cm is that?)
A new subdivision of 1500 houses is being planned. What size water main would be needed?
3.
4.
In chemistry you learned Boyle's Law, which states that the volume of a fixed amount of gas (at constant
temperature) is inversely proportional to the pressure of the gas.
a.
Write the particular equation expressing volume in terms of pressure if a pressure of 46 pounds per
square inch (psi) compresses the gas to a volume of 360 cubic feet.
b.
What pressure would be necessary to compress the gas to a volume of 276 cubic feet?
The strength of a radio signal received from the transmitter varies inversely with the square of your distance
from the transmitter.
a.
Write the particular equation expressing strength in terms of distance if the strength is 1000 units at a
distance of 2 km.
b.
What is the strength 10 kilometers from the transmitter?
c.
Predict the strength 100 kilometers from the transmitter?