Writing Equations worksheet with four real-world word problems for students to solve by defining variables and writing equations.

Let's solve each problem step by step from the worksheet titled "Writing Equations". The goal is to define a variable and write an equation for each situation.

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1. Tina wants to sell 30 items for her fundraiser. She knows that she has five days left to sell. Write an equation to find how many items she must sell per day in order to reach her goal.

- Define Variable:
Let $ x $ = number of items sold per day

- Equation:
Total items to sell = items per day × number of days
$ 5x = 30 $

✔ Answer:
- Variable: $ x $ = number of items sold per day
- Equation: $ 5x = 30 $

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2. Jerome has $28 in his pocket. He wants to buy as many candy bars as he can for $1.75 each. Write an equation to show how many candy bars he can buy.

- Define Variable:
Let $ x $ = number of candy bars

- Equation:
Cost per candy bar × number of candy bars = total money
$ 1.75x = 28 $

✔ Answer:
- Variable: $ x $ = number of candy bars
- Equation: $ 1.75x = 28 $

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3. George and his two friends each purchased popcorn at the movies. Each popcorn costs $6.25. What was the total amount spent on popcorn?

- Define Variable:
Let $ x $ = total cost of popcorn

- Equation:
Number of people × cost per popcorn = total cost
There are 3 people (George + 2 friends), so:
$ 3 \times 6.25 = x $
Or written as: $ x = 3(6.25) $

Alternatively, if you want to express it algebraically with a variable representing the cost:
But since the cost per popcorn is given, we can directly compute or write:

$ x = 3 \times 6.25 $ → $ x = 18.75 $

But the question asks to write an equation, not solve it.

So:
- Variable: $ x $ = total cost of popcorn
- Equation: $ x = 3 \times 6.25 $ or $ x = 18.75 $

But more generally, if we keep it symbolic:
Let’s say $ p $ = price per popcorn = 6.25, but since it's given, best to plug in.

✔ Answer:
- Variable: $ x $ = total cost of popcorn
- Equation: $ x = 3 \times 6.25 $ or $ x = 18.75 $

(Note: Some might prefer writing $ 3(6.25) = x $)

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4. Daylena needs to finish reading *The Giver* for her book report for Mr. Wagoner. She still has 112 pages. She knows that she can read 20 pages a night. Write an equation to show how many nights it will take Daylena to finish her book.

- Define Variable:
Let $ x $ = number of nights

- Equation:
Pages per night × number of nights = total pages
$ 20x = 112 $

✔ Answer:
- Variable: $ x $ = number of nights
- Equation: $ 20x = 112 $

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✔ Final Answers Summary:

| Problem | Variable | Equation |
|--------|---------|---------|
| 1 | $ x $ = number of items sold per day | $ 5x = 30 $ |
| 2 | $ x $ = number of candy bars | $ 1.75x = 28 $ |
| 3 | $ x $ = total cost of popcorn | $ x = 3 \times 6.25 $ or $ x = 18.75 $ |
| 4 | $ x $ = number of nights | $ 20x = 112 $ |

These equations model each real-world situation using variables and relationships between quantities. You can solve them further if needed (e.g., divide both sides), but the task only asked to write the equation.

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