Translating Word Problems into Equations: Beginning Algebra
General Approach to Solving Word Problems
1. Read the problem once - like it’s a story.
Then read it again, as if your life depends on it!
2. Write down pertinent information. You may have to draw a picture.
3. Assign a variable to the unknown.
“let x be the unknown”
If there is more than one unknown, try assigning your variable to the smallest
unknown. Then build your other unknown(s) from this variable.
For instance, if you know that one value is 5 pounds more than another,
“let x be the smaller unknown and let x+5 be the larger unknown”
4. Write an equation using your unknown(s) and hints that the problem gives you.
5. Solve your equation.
6. Determine if your answer makes sense.
If your problem asks for the number of dogs at the dog pound, and you get an answer
of − 5 , something is wrong.
Many of the word problems in pre-algebra can be classified as translation problems.
To successfully work “translation” word problems, you must have mastery over “math
words” and what they mean.
The following phrases represent addition:
x plus y
x more than y
x increased by y
the sum of x and y
x added to y
x more than y
the total of x and y
x
y
x
x
y
y
x
+
+
+
+
+
+
+
y
x
y
y
x
x
y
The following phrases represent subtraction:
x minus y
x
x less than y
y
x decreased by y
x
the difference of x and y
x
x subtracted from y
y
x less than y
y
x take away y
x
-
y
x
y
y
x
x
y
The following phrases represent multiplication:
x• y
x times y
x• y
the product of x and y
x• y
x of y
2• x
twice x
y•x
x multiplied by y
The following phrases represent division:
x divided by y
the quotient of x and y
Other:
the reciprocal of a number
the opposite of a number
x
y
x
y
1
x
−x