Exercise 35 Page 580

Practice makes perfect

a In the percent proportion, the ratio of the part a to the whole x is equal to the percent p written as a fraction.

a/x=p/100 If we are given any two of these three variables we can find the third one. In this exercise we are given the value a= 112 and percent p= 42, and we are looking for x.

a/x=p/100

SubstituteII

a= 112, p= 72

112/x=42/100

CrossMult

Cross multiply

11 200 = 42x

DivEqn

.LHS /42.=.RHS /42.

11 200/42 = x

RearrangeEqn

Rearrange equation

x = 11 200/42

ReduceFrac

a/b=.a /14./.b /14.

x = 800/3

FracToMixed

Write fraction as a mixed number

x = 266 23

WriteDec

Write as a decimal

x = 266.666...

RoundDec

Round to 2 decimal place(s)

x ≈ 266.67

This means that about 112 is 42 % of about 266.67.

b In the percent proportion, the ratio of the part a to the whole b is equal to the percent x written as a fraction.

a/b=x/100 If we are given any two of these three variables we can find the third one. In this exercise we are given the values a= 42 and b= 112, and we are looking for the percent x.

a/b=x/100

SubstituteII

a= 42, p= 112

42/112=x/100

MultEqn

LHS * 100=RHS* 100

42/112* 100 = x

MoveRightFacToNum

a/c* b = a* b/c

4200/112 = x

ReduceFrac

a/b=.a /56./.b /56.

75/2 = x

FracToMixed

Write fraction as a mixed number

37 12 = x

WriteDec

Write as a decimal

37.5 = x

RearrangeEqn

Rearrange equation

x = 37.5

This means that about 42 is 37.5 % of 112.

c In the percent proportion, the ratio of the part a to the whole b is equal to the percent x written as a fraction.

a/b=x/100 If we are given any two of these three variables we can find the third one. In this exercise we are given the values a= 27 and b= 100, and we are looking for the percent x.

a/b=x/100

SubstituteII

a= 27, p= 100

27/100=x/100

MultEqn

LHS * 100=RHS* 100

27 = x

RearrangeEqn

Rearrange equation

x = 27

This means that about 27 is 27 % of 100.

d In the percent proportion, the ratio of the part a to the whole b is equal to the percent x written as a fraction.

x/b=p/100 If we are given any two of these three variables we can find the third one. In this exercise, we are given the value b= 500 and the percent p = 27, and we are looking for the value x.

x/b=p/100

SubstituteII

b= 500, p= 27

x/500=27/100

MultEqn

LHS * 500=RHS* 500

x = 27/100 * 500

MoveRightFacToNum

a/c* b = a* b/c

x = 13 500/100

CalcQuot

Calculate quotient