Writing algebraic expressions from word problems worksheet with ... - Free Printable

Let's solve each problem step by step, writing both the algebraic expression and then substituting the given numbers to find the numerical expression and answer.

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1. Mr. Swanson has c students in his math class. One day, he picks up five new students. Write an expression for the new number of students in the class.

- Algebraic Expression:
$ c + 5 $

- Given: There were 27 students originally → $ c = 27 $

- Numerical Expression:
$ 27 + 5 $

- Answer:
$ 32 $

✔ Final Answer: 32 students

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2. Pratap has six times as many coins in his coin collection as Yoshiko. Yoshiko has y coins. Write an expression for the number of coins Pratap has.

- Algebraic Expression:
$ 6y $

- Given: Yoshiko has 47 coins → $ y = 47 $

- Numerical Expression:
$ 6 \times 47 $

- Answer:
$ 282 $

✔ Final Answer: 282 coins

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3. In a one-hour run-a-thon, Ayana runs 13 laps less than Emma. Write an expression for the number of laps Ayana runs.

Let’s choose a variable:
Let $ e $ = number of laps Emma runs

- Algebraic Expression:
$ e - 13 $

- Given: Emma runs 32 laps → $ e = 32 $

- Numerical Expression:
$ 32 - 13 $

- Answer:
$ 19 $

✔ Final Answer: 19 laps

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4. Nicki’s age is equal to the quotient of Granny’s age and six. Write an expression for Nicki’s age.

Let’s choose a variable:
Let $ g $ = Granny’s age

- Algebraic Expression:
$ \frac{g}{6} $

- Given: Granny is 72 years old → $ g = 72 $

- Numerical Expression:
$ \frac{72}{6} $

- Answer:
$ 12 $

✔ Final Answer: 12 years old

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5. The number of students in the 8th grade class is $ \frac{2}{3} $ of the number of students in the 7th grade class. Write an expression for the number of students in 8th grade.

Let’s choose a variable:
Let $ s $ = number of students in 7th grade

- Algebraic Expression:
$ \frac{2}{3}s $

- Given: 7th grade has 96 students → $ s = 96 $

- Numerical Expression:
$ \frac{2}{3} \times 96 $

- Answer:
$ \frac{2}{3} \times 96 = 64 $

✔ Final Answer: 64 students

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✔ Summary of Answers:

| Problem | Algebraic Expression | Numerical Expression | Answer |
|--------|----------------------|-----------------------|--------|
| 1 | $ c + 5 $ | $ 27 + 5 $ | 32 |
| 2 | $ 6y $ | $ 6 \times 47 $ | 282 |
| 3 | $ e - 13 $ | $ 32 - 13 $ | 19 |
| 4 | $ \frac{g}{6} $ | $ \frac{72}{6} $ | 12 |
| 5 | $ \frac{2}{3}s $ | $ \frac{2}{3} \times 96 $ | 64 |

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