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Mathematics LibreTexts

2.2E: Exercises

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Practice Makes Perfect

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution.

Exercise 2.2E.1

8x=56

Answer

x=7

Exercise 2.2E.2

7p=63

Exercise 2.2E.3

5c=55

Answer

c=11

Exercise 2.2E.4

9x=27

Exercise 2.2E.5

809=15y

Answer

y=80915

Exercise 2.2E.6

731=19y

Exercise 2.2E.7

37p=541

Answer

p=54137

Exercise 2.2E.8

19m=586

Exercise 2.2E.9

0.25z=3.25

Answer

z= 13

Exercise 2.2E.10

0.75a=11.25

Exercise 2.2E.11

13x=0

Answer

x=0

Exercise 2.2E.12

24x=0

Exercise 2.2E.13

x4=35

Answer

x=140

Exercise 2.2E.14

z2=54

Exercise 2.2E.15

20=q5

Answer

q=100

Exercise 2.2E.16

c3=12

Exercise 2.2E.17

y9=16

Answer

y=144

Exercise 2.2E.18

q6=38

Exercise 2.2E.19

m12=45

Answer

m=540

Exercise 2.2E.20

24=p20

Exercise 2.2E.21

y=6

Answer

y=6

Exercise 2.2E.22

u=15

Exercise 2.2E.23

v=72

Answer

v=72

Exercise 2.2E.24

x=39

Exercise 2.2E.25

23y=48

Answer

y=72

Exercise 2.2E.26

35r=75

Exercise 2.2E.27

58w=40

Answer

w=64

Exercise 2.2E.28

24=34x

Exercise 2.2E.29

25=110a

Answer

a=4

Exercise 2.2E.30

13q=56

Exercise 2.2E.31

710x=143

Answer

x=203

Exercise 2.2E.32

38y=14

Exercise 2.2E.33

712=34p

Answer

p=79

Exercise 2.2E.34

1118=56q

Exercise 2.2E.35

518=109u

Answer

u=14

Exercise 2.2E.36

720=74v

Solve Equations That Require Simplification

In the following exercises, solve each equation requiring simplification.

Exercise 2.2E.37

10016=4p10pp

Answer

p=12

Exercise 2.2E.38

187=5t9t6t

Exercise 2.2E.39

78n34n=9+2

Answer

n=88

Exercise 2.2E.40

512q+12q=253

Exercise 2.2E.41

0.25d+0.10d=60.75

Answer

d=15

Exercise 2.2E.42

0.05p0.01p=2+0.24

Exercise 2.2E.43

10(q4)57=93

Answer

q=11

Exercise 2.2E.44

12(d5)29=43

Exercise 2.2E.45

10(x+4)19=85

Answer

x=725

Exercise 2.2E.46

15(z+9)11=75

Mixed Practice

In the following exercises, solve each equation.

Exercise 2.2E.47

910x=90

Answer

x=100

Exercise 2.2E.48

512y=60

Exercise 2.2E.49

y+46=55

Answer

y=9

Exercise 2.2E.50

x+33=41

Exercise 2.2E.51

w2=99

Answer

w=198

Exercise 2.2E.52

s3=60

Exercise 2.2E.53

27=6a

Answer

a=92

Exercise 2.2E.54

a=7

Exercise 2.2E.55

x=2

Answer

x=2

Exercise 2.2E.56

z16=59

Exercise 2.2E.57

m41=14

Answer

m=27

Exercise 2.2E.58

0.04r=52.60

Exercise 2.2E.59

63.90=0.03p

Answer

p=2130

Exercise 2.2E.60

15x=120

Exercise 2.2E.61

84=12z

Answer

y=7

Exercise 2.2E.62

19.36=x0.2x

Exercise 2.2E.63

c0.3c=35.70

Answer

c=51

Exercise 2.2E.64

y=9

Exercise 2.2E.65

x=8

Answer

x=8

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

Exercise 2.2E.66

187 is the product of 17 and m

Exercise 2.2E.67

133 is the product of 19 and n

Answer

133=19n;n=7

Exercise 2.2E.68

184 is the product of 23 and p

Exercise 2.2E.69

152 is the product of 8 and q

Answer

152=8q;q=19

Exercise 2.2E.70

u divided by 7 is equal to 49

Exercise 2.2E.71

r divided by 12 is equal to 48

Answer

r12=48;r=576

Exercise 2.2E.72

h divided by 13 is equal to 65

Exercise 2.2E.73

j divided by 20 is equal to 80

Answer

j20=80;j=1,600

Exercise 2.2E.74

The quotient c and 19 is 38.

Exercise 2.2E.75

The quotient of b and 6 is 18

Answer

b6=18;b=108

Exercise 2.2E.76

The quotient of h and 26 is 52

Exercise 2.2E.77

The quotient k and 22 is 66

Answer

k22=66;k=1,452

Exercise 2.2E.78

Five-sixths of y is 15

Exercise 2.2E.79

Three-tenths of x is 15

Answer

310x=15;x=50

Exercise 2.2E.80

Four-thirds of w is 36

Exercise 2.2E.81

Five-halves of v is 50

Answer

52v=50;v=20

Exercise 2.2E.82

The sum of nine-tenths and g is two-thirds.

Exercise 2.2E.83

The sum of two-fifths and f is one-half.

Answer

25+f=12;f=110

Exercise 2.2E.84

The difference of p and one-sixth is two-thirds.

Exercise 2.2E.85

The difference of q and one-eighth is three-fourths.

Answer

q18=34;q=78

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Exercise 2.2E.86

Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?

Exercise 2.2E.87

Balloons Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. How many balloons did she use in each bunch?

Answer

6 balloons

Exercise 2.2E.88

Tickets Mollie paid $36.25 for 5 movie tickets. What was the price of each ticket?

Exercise 2.2E.89

Shopping Serena paid $12.96 for a pack of 12 pairs of sport socks. What was the price of pair of sport socks?

Answer

$1.08

Exercise 2.2E.90

Sewing Nancy used 14 yards of fabric to make flags for one-third of the drill team. How much fabric, would Nancy need to make flags for the whole team?

Exercise 2.2E.91

MPG John’s SUV gets 18 miles per gallon (mpg). This is half as many mpg as his wife’s hybrid car. How many miles per gallon does the hybrid car get?

Answer

36 mpg

Exercise 2.2E.92

Height Aiden is 27 inches tall. He is 38 as tall as his father. How tall is his father?

Exercise 2.2E.92

Real estate Bea earned $11,700 commission for selling a house, calculated as 6100 of the selling price. What was the selling
price of the house?

Answer

$195,000

Everyday Math

Exercise 2.2E.93

Commissions Every week Perry gets paid $150 plus 12% of his total sales amount. Solve the equation
840=150+0.12(a1250) for a to find the total amount Perry must sell in order to be paid $840 one week.

Exercise 2.2E.94

Stamps Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 less than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−5)=9.45 for s, to find the number of 49-cent stamps Travis bought.

Answer

15 49-cent stamps

Writing Exercises

Exercise 2.2E.95

Frida started to solve the equation −3x=36 by adding 3 to both sides. Explain why Frida’s method will not solve the equation.

Exercise 2.2E.96

Emiliano thinks x=40 is the solution to the equation 12x=80. Explain why he is wrong.

Answer

Answers will vary.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has five rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can...,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can...” reads “1) solve equations using the Division and Multiplication Properties of equality,” “2) solve equations that require simplification,” “3) translate to an equation and solve,” and “4) translate and solve applications.” The rest of the cells are blank.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?


This page titled 2.2E: Exercises is shared under a not declared license and was authored, remixed, and/or curated by OpenStax.

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