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Three-fifths of the members of the school choir are women. If there are $24$ women, what is the total number of choir members?
Zachary has $25$ country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?
Zachary has 125 CDs.
One-fourth of the candies in a bag of are red. If there are $23$ red candies, how many candies are in the bag?
There are $16$ girls in a school club. The number of girls is $4$ more than twice the number of boys. Find the number of boys in the club.
There are 6 boys in the club.
There are $18$ Cub Scouts in Troop $645.$ The number of scouts is $3$ more than five times the number of adult leaders. Find the number of adult leaders.
Lee is emptying dishes and glasses from the dishwasher. The number of dishes is $8$ less than the number of glasses. If there are $9$ dishes, what is the number of glasses?
There are 17 glasses.
The number of puppies in the pet store window is twelve less than the number of dogs in the store. If there are $6$ puppies in the window, what is the number of dogs in the store?
After $3$ months on a diet, Lisa had lost $\text{12\%}$ of her original weight. She lost $21$ pounds. What was Lisa's original weight?
Lisa's original weight was 175 pounds.
Tricia got a $\text{6\%}$ raise on her weekly salary. The raise was $\text{\$30}$ per week. What was her original weekly salary?
Tim left a $\text{\$9}$ tip for a $\text{\$50}$ restaurant bill. What percent tip did he leave?
18%
Rashid left a $\text{\$15}$ tip for a $\text{\$75}$ restaurant bill. What percent tip did he leave?
Yuki bought a dress on sale for $\text{\$72}.$ The sale price was $\text{60\%}$ of the original price. What was the original price of the dress?
The original price was $120.
Kim bought a pair of shoes on sale for $\text{\$40.50}.$ The sale price was $\text{45\%}$ of the original price. What was the original price of the shoes?
Solve Number Problems
In the following exercises, solve each number word problem.
The sum of a number and nine is $17.$ Find the number.
The difference of a number and twelve is $3.$ Find the number.
15
The difference of a number and eight is $4.$ Find the number.
The sum of three times a number and eight is $23.$ Find the number.
5
The sum of twice a number and six is $14.$ Find the number.
The difference of twice a number and seven is $17.$ Find the number.
12
The difference of four times a number and seven is $21.$ Find the number.
Three times the sum of a number and nine is $12.$ Find the number.
−5
Six times the sum of a number and eight is $30.$ Find the number.
One number is six more than the other. Their sum is forty-two. Find the numbers.
18, 24
One number is five more than the other. Their sum is thirty-three. Find the numbers.
The sum of two numbers is twenty. One number is four less than the other. Find the numbers.
8, 12
The sum of two numbers is twenty-seven. One number is seven less than the other. Find the numbers.
A number is one more than twice another number. Their sum is negative five. Find the numbers.
−2, −3
One number is six more than five times another. Their sum is six. Find the numbers.
The sum of two numbers is fourteen. One number is two less than three times the other. Find the numbers.
4, 10
The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.
One number is fourteen less than another. If their sum is increased by seven, the result is $85.$ Find the numbers.
32, 46
One number is eleven less than another. If their sum is increased by eight, the result is $71.$ Find the numbers.
The sum of two consecutive integers is $77.$ Find the integers.
38, 39
The sum of two consecutive integers is $89.$ Find the integers.
The sum of two consecutive integers is $\mathrm{-23}.$ Find the integers.
−11, −12
The sum of two consecutive integers is $\mathrm{-37}.$ Find the integers.
The sum of three consecutive integers is $78.$ Find the integers.
25, 26, 27
The sum of three consecutive integers is $60.$ Find the integers.
Find three consecutive integers whose sum is $\mathrm{-36}.$
−11, −12, −13
Find three consecutive integers whose sum is $\mathrm{-3}.$
Shopping Patty paid $\text{\$35}$ for a purse on sale for $\text{\$10}$ off the original price. What was the original price of the purse?
The original price was $45.
Shopping Travis bought a pair of boots on sale for $\text{\$25}$ off the original price. He paid $\text{\$60}$ for the boots. What was the original price of the boots?
Shopping Minh spent $\text{\$6.25}$ on $5$ sticker books to give his nephews. Find the cost of each sticker book.
Each sticker book cost $1.25.
Shopping Alicia bought a package of $8$ peaches for $\text{\$3.20}.$ Find the cost of each peach.
Shopping Tom paid $\text{\$1,166.40}$ for a new refrigerator, including $\text{\$86.40}$ tax. What was the price of the refrigerator before tax?
The price of the refrigerator before tax was $1,080.
Shopping Kenji paid $\text{\$2,279}$ for a new living room set, including $\text{\$129}$ tax. What was the price of the living room set before tax?
Write a few sentences about your thoughts and opinions of word problems. Are these thoughts positive, negative, or neutral? If they are negative, how might you change your way of thinking in order to do better?
Answers will vary.
When you start to solve a word problem, how do you decide what to let the variable represent?
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ If most of your checks were:
…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.
…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?
…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.
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