Elementary Algebra

Lynn Marecek

Chapter 3

Math Models - all with Video Answers

Educators

Section 1

Use a Problem-Solving Strategy

Problem 1

In the following exercises, prepare the lists described.
List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.

GH

Gerry Hsu

Numerade Educator

Problem 2

In the following exercises, prepare the lists described.
List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.

GH

Gerry Hsu

Numerade Educator

Problem 3

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
Two-thirds of the children in the fourth-grade class are girls. If there are 20 girls, what is the total number of children in the class?

Teresa Fuston

Numerade Educator

Problem 4

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
Three-fifths of the members of the school choir are women. If there are 24 women, what is the total number of choir members?

Teresa Fuston

Numerade Educator

Problem 5

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
Zachary has 25 country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?

Teresa Fuston

Numerade Educator

Problem 6

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
One-fourth of the candies in a bag of M\&M's are red. If there are 23 red candies, how many candies are in the bag?

Teresa Fuston

Numerade Educator

Problem 7

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.

Teresa Fuston

Numerade Educator

Problem 8

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
There are 18 Cub Scouts in Pack 645 . The number of scouts is three more than five times the number of adult leaders.
Find the number of adult leaders.

Teresa Fuston

Numerade Educator

Problem 9

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
Huong is organizing paperback and hardback books for her club’s used book sale. The number of paperbacks is 12 less than three times the number of hardbacks. Huong had 162 paperbacks. How many hardback books were there?

Teresa Fuston

Numerade Educator

Problem 10

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
Jeff is lining up children's and adult bicycles at the bike shop where he works. The number of children's bicycles is nine less than three times the number of adult bicycles. There are 42 adult bicycles. How many children's bicycles are there?

Sneha Ravi

Numerade Educator

Problem 11

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
Philip pays $$\$ 1,620$$ in rent every month. This amount is $$\$ 120$$ more than twice what his brother Paul pays for rent. How much does Paul pay for rent?

Teresa Fuston

Numerade Educator

Problem 12

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
Marc just bought an SUV for $$\$ 54,000$$. This is $$\$ 7,400$$ less than twice what his wife paid for her car last year. How much did his wife pay for her car?

Teresa Fuston

Numerade Educator

Problem 13

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
Laurie has $$\$ 46,000$$ invested in stocks and bonds. The amount invested in stocks is $$\$ 8,000$$ less than three times the amount invested in bonds. How much does Laurie have invested in bonds?

Teresa Fuston

Numerade Educator

Problem 14

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.
Erica earned a total of $$\$ 50,450$$ last year from her two jobs. The amount she earned from her job at the store was $$\$ 1,250$$ more than three times the amount she earned from her job at the college. How much did she earn from her job at the college?

Teresa Fuston

Numerade Educator

Problem 15

In the following exercises, solve each number word problem.
The sum of a number and eight is 12 . Find the number.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 16

In the following exercises, solve each number word problem.
The sum of a number and nine is $17 .$ Find the number.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 17

In the following exercises, solve each number word problem.
The difference of a number and 12 is three. Find the number.

Teresa Fuston

Numerade Educator

Problem 18

In the following exercises, solve each number word problem.
The difference of a number and eight is four. Find the number.

Teresa Fuston

Numerade Educator

Problem 19

In the following exercises, solve each number word problem.
The sum of three times a number and eight is $23 .$ Find the number.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 20

In the following exercises, solve each number word problem.
The sum of twice a number and six is $14 .$ Find the number.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 21

In the following exercises, solve each number word problem.
The difference of twice a number and seven is $17 .$ Find the number.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 22

In the following exercises, solve each number word problem.
The difference of four times a number and seven is 21 . Find the number.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 23

In the following exercises, solve each number word problem.
Three times the sum of a number and nine is 12. Find the number.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 24

In the following exercises, solve each number word problem.
Six times the sum of a number and eight is $30 .$ Find the number.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 25

In the following exercises, solve each number word problem.
One number is six more than the other. Their sum is 42 . Find the numbers.

Teresa Fuston

Numerade Educator

Problem 26

In the following exercises, solve each number word problem.
One number is five more than the other. Their sum is $33 .$ Find the numbers.

Teresa Fuston

Numerade Educator

Problem 27

In the following exercises, solve each number word problem.
The sum of two numbers is $20 .$ One number is four less than the other. Find the numbers.

Teresa Fuston

Numerade Educator

Problem 28

In the following exercises, solve each number word problem.
The sum of two numbers is 27 . One number is seven less than the other. Find the numbers.

Teresa Fuston

Numerade Educator

Problem 29

In the following exercises, solve each number word problem.
The sum of two numbers is -45 . One number is nine more than the other. Find the numbers.

Teresa Fuston

Numerade Educator

Problem 30

In the following exercises, solve each number word problem.
The sum of two numbers is -61 . One number is 35 more than the other. Find the numbers.

Teresa Fuston

Numerade Educator

Problem 31

In the following exercises, solve each number word problem.
The sum of two numbers is -316 . One number is 94 less than the other. Find the numbers.

Teresa Fuston

Numerade Educator

Problem 32

In the following exercises, solve each number word problem.
The sum of two numbers is -284 . One number is 62 less than the other. Find the numbers.

Teresa Fuston

Numerade Educator

Problem 33

In the following exercises, solve each number word problem.
One number is 14 less than another. If their sum is increased by seven, the result is 85 . Find the numbers.

Teresa Fuston

Numerade Educator

Problem 34

In the following exercises, solve each number word problem.
One number is 11 less than another. If their sum is increased by eight, the result is 71 . Find the numbers.

Teresa Fuston

Numerade Educator

Problem 35

In the following exercises, solve each number word problem.
One number is five more than another. If their sum is increased by nine, the result is $60 .$ Find the numbers.

Teresa Fuston

Numerade Educator

Problem 36

In the following exercises, solve each number word problem.
One number is eight more than another. If their sum is increased by $17,$ the result is $95 .$ Find the numbers.

Teresa Fuston

Numerade Educator

Problem 37

In the following exercises, solve each number word problem.
One number is one more than twice another. Their sum is -5 . Find the numbers.

Teresa Fuston

Numerade Educator

Problem 38

In the following exercises, solve each number word problem.
One number is six more than five times another. Their sum is six. Find the numbers.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 39

In the following exercises, solve each number word problem.
The sum of two numbers is $14 .$ One number is two less than three times the other. Find the numbers.

Teresa Fuston

Numerade Educator

Problem 40

In the following exercises, solve each number word problem.
The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 41

In the following exercises, solve each number word problem.
The sum of two consecutive integers is 77 . Find the integers.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 42

In the following exercises, solve each number word problem.
The sum of two consecutive integers is $89 .$ Find the integers.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 43

In the following exercises, solve each number word problem.
The sum of two consecutive integers is $-23 .$ Find the integers.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 44

In the following exercises, solve each number word problem.
The sum of two consecutive integers is -37 . Find the integers.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 45

In the following exercises, solve each number word problem.
The sum of three consecutive integers is $78 .$ Find the integers.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 46

In the following exercises, solve each number word problem.
The sum of three consecutive integers is $60 .$ Find the integers.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 47

In the following exercises, solve each number word problem.
Find three consecutive integers whose sum is -36 .

Amy Monaghan

Numerade Educator

Problem 48

In the following exercises, solve each number word problem.
Find three consecutive integers whose sum is -3 .

Amy Monaghan

Numerade Educator

Problem 49

In the following exercises, solve each number word problem.
Find three consecutive even integers whose sum is 258 .

Teresa Fuston

Numerade Educator

Problem 50

In the following exercises, solve each number word problem.
Find three consecutive even integers whose sum is 222 .

Teresa Fuston

Numerade Educator

Problem 51

In the following exercises, solve each number word problem.
Find three consecutive odd integers whose sum is 171 .

Teresa Fuston

Numerade Educator

Problem 52

In the following exercises, solve each number word problem.
Find three consecutive odd integers whose sum is 291 .

Teresa Fuston

Numerade Educator

Problem 53

In the following exercises, solve each number word problem.
Find three consecutive even integers whose sum is -36 .

Teresa Fuston

Numerade Educator

Problem 54

In the following exercises, solve each number word problem.
Find three consecutive even integers whose sum is -84 .

Teresa Fuston

Numerade Educator

Problem 55

In the following exercises, solve each number word problem.
Find three consecutive odd integers whose sum is -213 .

Teresa Fuston

Numerade Educator

Problem 56

In the following exercises, solve each number word problem.
Find three consecutive odd integers whose sum is -267 .

Teresa Fuston

Numerade Educator

Problem 57

Patty paid $$\$ 35$$ for a purse on sale for $$\$ 10$$ off the original price. What was the original price of the purse?

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 58

Travis bought a pair of boots on sale for $$\$ 25$$ off the original price. He paid $$\$ 60$$ for the boots. What was the original price of the boots?

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 59

Minh spent $$\$ 6.25$$ on five sticker books to give his nephews. Find the cost of each sticker book.

Sheryl Ezze

Numerade Educator

Problem 60

Alicia bought a package of eight peaches for $$\$ 3.20 .$$ Find the cost of each peach.

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 61

Tom paid $$\$ 1,166.40$$ for a new refrigerator, including $$\$ 86.40$$ tax. What was the price of the refrigerator?

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 62

Kenji paid $$\$ 2,279$$ for a new living room set, including $$\$ 129$$ tax. What was the price of the living room set?

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 63

What has been your past experience solving word problems?

GH

Gerry Hsu

Numerade Educator

Problem 64

When you start to solve a word problem, how do you decide what to let the variable represent?

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 65

What are consecutive odd integers? Name three consecutive odd integers between 50 and 60 .

Sneha Ravi

Numerade Educator

Problem 66

What are consecutive even integers? Name three consecutive even integers between -50 and -40 .

Sneha Ravi

Numerade Educator