412 CHAPTER 7 Rational Expressions and Functions
OBJECTIVE 5 Solve combined variation problems. There are many combi-
nations of direct and inverse variation, typically called combined variation.
Solving a Combined Variation ProblemBody mass index, or BMI, is used to assess a person’s level of fatness. A BMI from
19 through 25 is considered desirable. BMI varies directly as an individual’s weight
in pounds and inversely as the square of the individual’s height in inches.
A person who weighs 116.5 lb and is 64 in. tall has a BMI of 20. (The BMI is
rounded to the nearest whole number.) Find the BMI of a man who weighs 165 lb and
is 70 in. tall. (Source: Washington Post.)
Let Brepresent the BMI, wthe weight, and hthe height.
B=
kw
h^2
EXAMPLE 7
BMI varies directly as the weight.
BMI varies inversely as the square of the height.To find k, let and
Multiply by. Divide by 116.5.Use a calculator.Now find Bwhen and
Nearest whole numberThe man’s BMI is 24.
NOW TRYB=
70311652
702
L 24
k= 703,w= 165, h=70.
kL 703
k= 642
2016422
116.5
B=
kw
h^220 =
k 1 116.5 2
642
B=20, w= 116.5, h=64.
NOW TRY
EXERCISE 7
In statistics, the sample size
used to estimate a population
mean varies directly as the
variance and inversely as the
square of the maximum error
of the estimate. If the sample
size is 200 when the variance is
and the maximum error
of the estimate is 0.5 m, find
the sample size when the vari-
ance is and the maximum
error of the estimate is 0.1 m.
25 m^225 m^2
NOW TRY ANSWER
- 5000
Complete solution available
on the Video Resources on DVD
7.6 EXERCISES
Concept Check Use personal experience or intuition to determine whether the situation
suggests director inversevariation.
1.The number of lottery tickets you buy and your probability of winning that lottery
2.The rate and the distance traveled by a pickup truck in 3 hr
3.The amount of pressure put on the accelerator of a car and the speed of the car
4.The number of days from now until December 25 and the magnitude of the frenzy of
Christmas shopping
5.Your age and the probability that you believe in Santa Claus
6.The surface area of a balloon and its diameter
7.The number of days until the end of the baseball season and the number of home runs that
Albert Pujols has
8.The amount of gasoline you pump and the amount you pay