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Students practice writing algebraic expressions to solve real-world problems involving time, money, and distance.

A worksheet titled "Using Algebraic Expressions" with six word problems requiring students to write algebraic expressions for various scenarios, including time, money, and distance calculations.

A worksheet titled "Using Algebraic Expressions" with six word problems requiring students to write algebraic expressions for various scenarios, including time, money, and distance calculations.

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Show Answer Key & Explanations Step-by-step solution for: Using Algebraic Expressions - Word Problems - 6th Grade Algebra by ...
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It seems like the task involves writing algebraic expressions for various scenarios and solving problems based on those expressions. Since you mentioned that an image was uploaded, I'll provide a general explanation of how to approach each type of problem listed in the scenarios. If you can share more details or clarify any specific part, I can refine the solution further.

General Approach:


1. Identify the variable: Determine what the unknown quantity is and assign it a variable (e.g., \( x \)).
2. Write the expression: Use the given information to write an algebraic expression.
3. Solve the problem: Use the expression to answer the question.

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Detailed Solutions for Each Scenario:



#### 1. Farmer Tom's Eggs
- Scenario: Farmer Tom sold 15 eggs every hour. Write an expression for how many eggs he sold in \( d \) days.
- Expression: Since there are 24 hours in a day, the number of eggs sold in one day is \( 15 \times 24 \). Over \( d \) days, the total number of eggs sold is:
\[
15 \times 24 \times d = 360d
\]
- Question: How many eggs did he sell in 5 hours?
- In 5 hours, the number of eggs sold is:
\[
15 \times 5 = 75
\]

#### 2. Jason's Money
- Scenario: Jason has some money. His grandmother gives him another $18.00. Write an expression for how much money Jason has now.
- Expression: Let \( x \) be the amount of money Jason initially has. After receiving $18.00 from his grandmother, the total amount of money Jason has is:
\[
x + 18
\]
- Question: How much does he have if he started with $25.00?
- Substitute \( x = 25 \) into the expression:
\[
25 + 18 = 43
\]

#### 3. Lily's Puzzle
- Scenario: Lily is working on a 1,000-piece puzzle. She has already put out some of the pieces. Write an expression for how many pieces Lily has left.
- Expression: Let \( p \) be the number of pieces Lily has already put out. The total number of pieces in the puzzle is 1,000, so the number of pieces left is:
\[
1000 - p
\]
- Question: If Lily has put out 148 pieces, how many does she have left?
- Substitute \( p = 148 \) into the expression:
\[
1000 - 148 = 852
\]

#### 4. Carrie's Chocolates
- Scenario: Carrie’s Chocolate Shop puts 12 chocolates in each box they sell. Write an expression to show how many boxes they have.
- Expression: Let \( c \) be the total number of chocolates. Since each box contains 12 chocolates, the number of boxes is:
\[
\frac{c}{12}
\]
- Question: If the store has 1,200 chocolates, how many boxes can they make?
- Substitute \( c = 1200 \) into the expression:
\[
\frac{1200}{12} = 100
\]

#### 5. David's Running
- Scenario: David runs every day after school. Last week, he ran a total of 42 miles. Write an equation to show how far he ran this week.
- Expression: Let \( r \) be the number of days David ran last week. Since he ran a total of 42 miles, the distance he ran per day is:
\[
\frac{42}{r}
\]
- Question: If David ran 4 miles last week, how far did he run this week?
- If David ran 4 miles per day, then the number of days he ran last week is:
\[
r = \frac{42}{4} = 10.5
\]
However, since the number of days must be a whole number, we need to re-evaluate the context. Assuming he ran 4 miles per day for 10 days:
\[
4 \times 10 = 40 \text{ miles}
\]
So, he ran 42 miles in 10.5 days, which means he ran 4 miles per day.

#### 6. Lydia's Paycheck
- Scenario: Lydia’s neighbor pays her $22.00 to babysit Sunday afternoon. Write an equation to show how much money she makes.
- Expression: Let \( n \) be the number of Sundays Lydia babysits. The total amount of money she earns is:
\[
22n
\]
- Question: How much money does Lydia earn after 3 Sundays?
- Substitute \( n = 3 \) into the expression:
\[
22 \times 3 = 66
\]

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Final Answers:


1. Eggs sold in 5 hours: \( \boxed{75} \)
2. Jason's total money: \( \boxed{43} \)
3. Pieces left in the puzzle: \( \boxed{852} \)
4. Number of chocolate boxes: \( \boxed{100} \)
5. Distance ran per day: \( \boxed{4} \)
6. Money earned after 3 Sundays: \( \boxed{66} \)

If you have any specific questions or need further clarification, feel free to ask!
Parent Tip: Review the logic above to help your child master the concept of 6th grade algebra word problems worksheet.
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