Exercise 34 Page 305

We know that a person who weighs 160 pounds has about 4.6 quarts of blood. We need to find about how many quarts of blood are in the body of a person who weighs 175 pounds. We will follow a three-step plan.

1. We will find the constant of variation.
2.  We will write an equation that relates quarts of blood to weight.
3. We will determine the amount of blood in the body of a 175 pounds person by using the equation written in the second step.

Finding the Constant of Variation

Since the amount of blood in a person's body varies directly with body weight, we can find the constant of variation by dividing the amount of blood by the body weight. Let's name the constant of variation k.

k=Amount of Blood/Body Weight

SubstituteII

Amount of Blood= 4.6, Body Weight= 160

k=4.6/160

UseCalc

Use a calculator

k=0.02875

Therefore, the constant of variation is 0.02875.

Writing an Equation for the Direct Variation

The general form of the equation of a direct variation is as follows. y=kx In the equation, y represents the quarts of blood, x represents the body weight, and k is the constant of variation. We found the value of k in the first step, so we can write the equation. y=0.02875x

Determining the Amount of Blood

We want to find about how many quarts of blood are in the body of a person who weighs 175 pounds. Therefore, if we substitute 175 pounds for x into the equation we can find the amount of blood. Let's do it!

y=0.02875x

Substitute

x= 175

y=0.02875( 175)

Multiply

Multiply

y=5.03125

RoundDec

Round to 2 decimal place(s)

y≈ 5.03

There are about 5.03 quarts of blood in the body of a 175-pound person.