Worksheet for writing algebraic expressions from word problems.

Let's solve each problem step by step and provide the required expressions and answers.

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Problem 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:
The original number of students is \( c \). Adding 5 new students gives:
\[
c + 5
\]

#### Numerical Expression:
If there were originally 27 students (\( c = 27 \)):
\[
27 + 5
\]

#### Answer:
\[
27 + 5 = 32
\]

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Problem 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:
If Yoshiko has \( y \) coins, then Pratap has six times as many:
\[
6y
\]

#### Numerical Expression:
If Yoshiko has 47 coins (\( y = 47 \)):
\[
6 \times 47
\]

#### Answer:
\[
6 \times 47 = 282
\]

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Problem 3:

In a one-hour run-athon to raise money for the track team, Ayana runs 13 laps less than Emma. Write an expression for the number of laps Ayana runs.

#### Algebraic Expression:
Let \( E \) represent the number of laps Emma runs. Then Ayana runs 13 laps less:
\[
E - 13
\]

#### Numerical Expression:
If Emma runs 32 laps (\( E = 32 \)):
\[
32 - 13
\]

#### Answer:
\[
32 - 13 = 19
\]

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Problem 4:

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

#### Algebraic Expression:
Let \( G \) represent Granny’s age. Then Nicki’s age is the quotient of Granny’s age divided by 6:
\[
\frac{G}{6}
\]

#### Numerical Expression:
If Granny is 72 years old (\( G = 72 \)):
\[
\frac{72}{6}
\]

#### Answer:
\[
\frac{72}{6} = 12
\]

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Problem 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.

#### Algebraic Expression:
Let \( s \) represent the number of students in the 7th grade class. Then the number of students in the 8th grade class is:
\[
\frac{2}{3}s
\]

#### Numerical Expression:
If there are 96 students in the 7th grade (\( s = 96 \)):
\[
\frac{2}{3} \times 96
\]

#### Answer:
\[
\frac{2}{3} \times 96 = 64
\]

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Final Answers:

1. Algebraic Expression: \( c + 5 \)
- Numerical Expression: \( 27 + 5 \)
- Answer: \( 32 \)

2. Algebraic Expression: \( 6y \)
- Numerical Expression: \( 6 \times 47 \)
- Answer: \( 282 \)

3. Algebraic Expression: \( E - 13 \)
- Numerical Expression: \( 32 - 13 \)
- Answer: \( 19 \)

4. Algebraic Expression: \( \frac{G}{6} \)
- Numerical Expression: \( \frac{72}{6} \)
- Answer: \( 12 \)

5. Algebraic Expression: \( \frac{2}{3}s \)
- Numerical Expression: \( \frac{2}{3} \times 96 \)
- Answer: \( 64 \)

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Boxed Final Answers:

\[
\boxed{
\begin{array}{lll}
1. & \text{Algebraic Expression: } c + 5 & \text{Answer: } 32 \\
2. & \text{Algebraic Expression: } 6y & \text{Answer: } 282 \\
3. & \text{Algebraic Expression: } E - 13 & \text{Answer: } 19 \\
4. & \text{Algebraic Expression: } \frac{G}{6} & \text{Answer: } 12 \\
5. & \text{Algebraic Expression: } \frac{2}{3}s & \text{Answer: } 64 \\
\end{array}
}
\]