Lesson 3: Word Problems

Property

To solve word problems, first translate the word sentences into equations with variables, and then solve the equations using the properties of equality. Identify keywords to determine the correct operation.

Examples

• 'Seven more than $n$ is equal to 2.' translates to $n + 7 = 2$. Subtracting 7 from both sides gives $n = -5$.

• 'The difference of $p$ and 9 is $-15$.' translates to $p - 9 = -15$. Adding 9 to both sides gives $p = -6$.

Property

Use a Problem-Solving Strategy to Solve Word Problems.

1. Read the problem. Make sure all the words and ideas are understood.
2. Identify what we are looking for.
3. Name what we are looking for. Choose a variable to represent that quantity.
4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation.
5. Solve the equation using good algebra techniques.
6. Check the answer in the problem and make sure it makes sense.
7. Answer the question with a complete sentence.

Examples

• A shirt is on sale for 25 dollars, which is one-third of its original price. What was the original price? Let $p$ be the original price. The equation is $25 = \frac{1}{3}p$. Solving for $p$ gives $p=75$. The original price was 75 dollars.

• A book club has 17 women. The number of women is two more than three times the number of men. How many men are in the club? Let $m$ be the number of men. The equation is $17 = 3m + 2$. Solving for $m$ gives $m=5$. There are 5 men in the club.