WORD PROBLEMS
Translating from Words into Symbols
An equation can be used to solve a word problem if the problem is first
translated from words into algebraic symbols.
The following table tells which of the symbols +, -, ,  and = can be used
to replace certain word phrases.
+
the sum of
(the sum of a
and b is
a + b)
-
the difference of:
the difference
between
(the difference of
[between] a and
b is a - b)

the product
of
the quotient
of
(the product
of a and b is
a  b)
(the
quotient of
a and b is a
 b)
more than
less than
times
divided by
(6 more than
x is x + 6)
(6 less than x is
x - 6)
(a times b is
a  b)
(a divided
by b is a 
b)
increased by
decreased by
twice
half of
(x increased
by 6 is x+6)
(x decreased by
6 is x - 6)
means
means
exceeds
diminished by
double
one-third of
means is
means decreased
means
means
more than
by
multiply by 2
multiply by 2
=

is equal
to
equals
the result
is
divide by 2
divide by 3
is
General Procedure for Solving Word Problems
1) Read the problem carefully and decide the one basic value to be found
(the unknown)
2) Represent the unknown by a letter. Using a “LET STATEMENT” at the
beginning of the solution write the words that the letter stands for.
(Of more than one value is to be found, represent all the unknown
values in terms of the one basic unknown)
ie) Find both Tom and Sally’s weights if Sally weighs 6lbs less
than Tom…..
Let Tom’s weight = x
then Sally’s weight = x - 6
3) Translate each word phrase into algebraic symbols, using the previous table
as a guide, so that an algebraic open sentence results.
4) Find the solution set for the open sentence. (Solve for the variable(s) and
then substitute it back into your “Let statement”…yes you must show work)
5) Check each element of the solution in the words of the problem (use your
brain and your common sense and make sure that your solutions are
reasonable!!!)
6) Write the answer to the problem in the form of a word sentence.
( x = 5 is not enough….“The number is 5” otherwise…minus 1 )
…..YES, you must show all the steps
EX:
1) If three times a number is increased by 4, the result is the the same as when
five times the number is decreased by 20. What is the number?
2) The larger of two groups has twice the number of members of the smaller
group. If the smaller group is increased by 4, the result is 6 less than the larger
number. Find the number of members in each group.
3) Two numbers are in the ratio of 4:7. If the sum of the numbers is 33, find
the numbers.
Name ____________________________
Algebra I - Pd ____
Date _______________
Word Problems
Solve each of the following word problems and check. Do work on looseleaf.
1) The sum of seven times a number and five is 47. Find the number.
2) If ten times a number is decreased by six the result is 104. Find the number.
3) If four times a number is increased by five, the result is 41. Find the number.
4) If five times a number is decreased by 13, the result is equal to twice the number
increased by 11. Find the number.
5) Eight times a number equals 35 more than the number. Find the number.
6) Six times a number equals three times the number increased by 24. Find the number.
7) Twice a number is equal to 35 more than seven times the number. Find the number.
8) If a number is multiplied by 7, the result is the same as when 25 is added to twice the
number. Find the number.
9) If twice a number is subtracted from 132, the result is the same as when fifteen is added to
twice the number. Find the number.
10) If three is added to five times a number the result is the same as when fifteen is added to
twice the number. Find the number.
11) If three times a number is increased by five, the result is the same as when 77 is
decreased by 9 times the number. Find the number.
12) One number is for more than another. If four times the smaller number is decreased by
twice the larger number, the result is 12. Find both numbers.