Chapter Twenty-One — Rational Equations and Inequalities
The Humongous Book of Algebra Problems
Direct and Indirect Variation
Turn a word problem into a rational equation
21.21 Assume that the value of x varies directly with the value of y according to
the constant of proportionality k. Identify two equations that describe the
relationship between x and y.
If x and y vary proportionally, then y = kx and .
Note: Problems 21.22–21.23 refer to the direct variation relationship described below.
21.22 A professional sports team notes that the ambient crowd noise at home
games is directly proportional to the attendance at those games. During one
game, the cheering of a maximum capacity crowd of 75,000 fans averages 90
decibels. Identify the constant of proportionality k.
Let a represent attendance and n represent the noise (in decibels) generated by
that population. If n varies directly with a, then (according to Problem 21.21)
n = ka. Substitute n = 90 and a = 75,000 into the equation and solve for k.
Note: Problems 21.22–21.23 refer to the direct variation relationship described in Problem
21.23 Approximately how loud is a crowd of 62,000 fans?
Substitute a = 62,000 and k = 0.0012 into the variation equation n = ka to
the same thing as
k = 2. According
to the equation
y = kx, y is always twice
as big as x. Because
y is always two times
as large as x, y ÷ x
always equals 2.
of k (and the
equation n = ka
that you plug it into)
come from Problem