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.
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Step-by-step solution for: Using Algebraic Expressions - Word Problems - 6th Grade Algebra by ...
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Show Answer Key & Explanations
Step-by-step solution for: Using Algebraic Expressions - Word Problems - 6th Grade Algebra by ...
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.
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.
---
#### 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:
\[
22 \times 3 = 66
\]
---
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!
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.
---
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:
\[
22 \times 3 = 66
\]
---
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.