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Chapter 9 Word Problems
Basic Word Problems Introduction
Word problems come in several types. You will find several basic types of word problems in every
algebra book. Each different type has a slightly different set up but they all have many things in
common. Many of these basic types are not exactly like the word problems you will encounter in
nursing, electronics, business or even in your daily life. The basic types of word problems that we
use in this chapter have been selected to help teach you the basic procedures and concepts
which can be used in almost all word problems you may encounter in other areas of study. If you
master these you will often be able to solve other problems that differ from the types you have
learned in this course. This unit will show you step by step what to do to set up and solve the types
of word problems that we will cover.
How do you start to set up a word problem?
1. Read the problem all the way through once to see what type of problem it is.
2. Determine the two (or three) unknown quantities that you are being asked to find the values for.
Look for a sentence that asks you to find something or for a sentence with a question mark ?
3. Look for a sentence that compares the first two unknowns. The sentence that does this will state
things like “the numbers of dogs is 5 more than the number of cats”
4. Start the problem with Let “something” = x. We let x equal the quantity that is being used as the
basis for comparison. The quantity mentioned second in the sentence is almost always the
quantity the other quantities are compared to. This means that the quantity mentioned second
is set equal to x and the first quantity will be an expression with x in it.
4. Express the second unknown as a statement with the unknown written in terms of x by using the
translations on the next page.
5. Go back and read the problem again. A second sentence will help you set up an equation. It is
very common for that sentence to state what the total value of the unknowns is.
6. Solve the equation for the unknown variable.
7. Plug the value of x into the expression for the other unknowns to find their values.
8. State the solution by listing each unknown and its value.
9. Check your solution in the original problem to see if the solution works.
Chapter 9
© 2015 Eitel
Translating Word Problems
How to translate English Statements into Algebraic Expressions
Listed below are examples of some of the most common statements found in word problems. Each
English statement has been translated into an algebra statement with x as the unknown. You should
study the order of the unknown term and the constant term. It is a common mistake to reverse the
order.
English Statement
Algebra Expression
is, was, will be
=
times, of, product
multiply
twice a number or two times a number *
2x
three times a number *
3x
four times a number *
4x
more than, increased by, sum
add
6 more than a number *
x+6
(6 added at the end)
7 more than twice a number *
2x + 7
(7 added at the end)
4 more than 3 times a number *
a number increased by 10
the sum of a number and 7
3x + 4
x + 10
x+7
(4 added at the end)
less than, decreased by
subtract: order is very important
5 less than a number *
x–5
(5 subtracted at the end)
2x – 4
(4 subtracted at the end)
7 less than three times a number
3x – 7
(7 subtracted at the end)
(4 subtracted at the end)
a number decreased by 10
2x – 8
x – 10
4 less than twice a number
*
*
8 less than two times a number *
Ratio (quotient)
the ratio of Doctors to Nurses
division
D
N
the ratio of Cars to Trucks
C
T
the ratio of Miles to Gallons
M
G
Chapter 9
© 2015 Eitel
Page 3 Translation Problems
Translate each English expression into an algebraic expression.
English
Algebra
English
Algebra
1.
5 more than a number
_________
16. 12 less than 5 times a number
_________
2.
5 times a number
_________
17. 2 less than 3 times a number
_________
3.
1 more than a number
_________
18. 4 more than 5 times a number
_________
4.
12 less than a number
_________
19. 1 more than twice a number
_________
5.
3 times a number
_________
20. 6 less than 7 times a number
_________
6.
7 more than a number
_________
21. 3 more than twice a number
_________
7.
8 less than a number
_________
22. 9 more than 3 times a number
_________
8.
4 times a number
_________
23. 12 less than 3 times a number
_________
9.
10 less than a number
_________
24.
9 less than 6 times a number
_________
10.
twice a number
_________
25.
6 more than 5 times a number
_________
11.
8 times a number
_________
26. 1 more than 4 times a number
_________
12. 12 more than a number
_________
27.
_________
13. 20 less than a number
_________
28. 5 less than twice a number
_________
14. 15 more than a number
_________
29. 7 more than twice a number
_________
15.
_________
30. 4 less than 7 times a number
_________
5 less than a number
Chapter 9
9 more than 6 times a number
© 2015 Eitel
9 – 3 Answers
1. x + 5
7. x – 8
13. x – 20
19. 2x + 1
25. 5x + 6
Chapter 9
2. 5x
8. 4x
14. x + 15
20. 7x – 6
26. 4x + 1
3. x + 1
9. x – 10
15. x – 5
21. 2x + 3
27. 6x + 9
4. x – 12
10. 2x
16. 5x – 12
22. 3x + 9
28. 2x – 5
5. 3x
11. 8x
17. 3x – 2
23. 3x – 12
29. 2x + 7
6. x + 7
12. x + 12
18. 5x + 4
24. 6x – 9
30. 7x – 4
© 2015 Eitel