EXAMPLE
Pete bought a shirt on sale for $
18
18, which is one-half the original price. What was the original price of the shirt?
Solution:
Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.
In this problem, do you understand what is being discussed? Do you understand every word?
Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!
In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.
Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.
Let
p
=
p= the original price of the shirt
Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.
The top line reads:
Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.
Write the equation.
18
=
1
2
p
18=12p
Multiply both sides by 2.
2
⋅
18
=
2
⋅
1
2
p
2⋅18=2⋅1Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.
Let
p
=
p= the original price of the shirt
Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.
The top line reads:Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.
Write the equation.
18
=
1
2
p
18=12p
Multiply both sides by 2.
2
⋅
18
=
2
⋅
1
2
p
2⋅18=2⋅12p
Simplify.
36
=
p
36=pStep 6. Check the answer in the problem and make sure it makes sense.
We found that
p
=
36
p=36, which means the original price was
$36
$36. Does
$36
$36 make sense in the problem? Yes, because
18
18 is one-half of
36
36, and the shirt was on sale at half the original price.Step 7. Answer the question with a complete sentence.
The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was
$36
$36.”
If this were a homework exercise, our work might look like this:
The top reads,
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