The image contains a worksheet titled "Writing Equations," where students are tasked with defining variables and writing equations to solve real-world problems. Below is a detailed explanation of each problem, including the solution and reasoning:
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Problem 1:
Scenario:
Jenna wants to raise $30 for her fundraiser. She knows she has five days left to sell items. Write an equation to find how many items she must sell per day in order to reach her goal.
####
Solution:
1.
Define Variable:
- Let \( n \) represent the number of items Jenna needs to sell per day.
2.
Equation:
- Jenna has 5 days to sell items, and she needs to raise $30.
- If she sells \( n \) items per day, then over 5 days, she will sell \( 5n \) items.
- The total amount raised from selling items is given as $30.
- Therefore, the equation is:
\[
5n = 30
\]
####
Explanation:
- The variable \( n \) represents the number of items sold per day.
- Multiplying \( n \) by 5 gives the total number of items sold over 5 days.
- Setting this equal to 30 ensures that the total amount raised matches Jenna's goal.
---
Problem 2:
Scenario:
Jessica has $28 in her pocket. She wants to buy as many candy bars as she can at $1.25 each. Write an equation to show how many candy bars she can buy.
####
Solution:
1.
Define Variable:
- Let \( n \) represent the number of candy bars Jessica can buy.
2.
Equation:
- Each candy bar costs $1.25.
- If Jessica buys \( n \) candy bars, the total cost will be \( 1.25n \).
- Jessica has $28 to spend, so the total cost cannot exceed $28.
- Therefore, the equation is:
\[
1.25n = 28
\]
####
Explanation:
- The variable \( n \) represents the number of candy bars Jessica can purchase.
- Multiplying \( n \) by $1.25 gives the total cost of the candy bars.
- Setting this equal to $28 ensures that Jessica spends all her money without exceeding it.
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Problem 3:
Scenario:
George and his two friends each purchased popcorn at the movies. Each popcorn costs $6.25. What was the total amount spent on popcorn?
####
Solution:
1.
Define Variable:
- Let \( t \) represent the total cost of popcorn.
2.
Equation:
- George and his two friends make a total of 3 people.
- Each person bought one popcorn, and each popcorn costs $6.25.
- Therefore, the total cost \( t \) is:
\[
t = 3 \times 6.25
\]
- Simplifying:
\[
t = 18.75
\]
####
Explanation:
- The variable \( t \) represents the total cost of popcorn.
- Since there are 3 people and each popcorn costs $6.25, multiplying 3 by $6.25 gives the total cost.
- The equation directly calculates the total amount spent.
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Problem 4:
Scenario:
Dayna needs to finish reading *That Glass* for her book report. Waggoner is 112 pages long. She knows that she can read 30 pages each night before bed. Write an equation to show how many nights it will take Dayna to finish her book.
####
Solution:
1.
Define Variable:
- Let \( n \) represent the number of nights Dayna needs to read.
2.
Equation:
- Dayna reads 30 pages per night.
- The total number of pages in the book is 112.
- If she reads \( n \) nights, the total number of pages read will be \( 30n \).
- To finish the book, the total pages read must equal 112.
- Therefore, the equation is:
\[
30n = 112
\]
####
Explanation:
- The variable \( n \) represents the number of nights Dayna needs to read.
- Multiplying \( n \) by 30 gives the total number of pages read.
- Setting this equal to 112 ensures that Dayna finishes the entire book.
---
Final Answer:
\[
\boxed{
\begin{aligned}
1. & \quad 5n = 30 \\
2. & \quad 1.25n = 28 \\
3. & \quad t = 18.75 \\
4. & \quad 30n = 112
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of equation word problems worksheet.
