Have you ever carried a backpack hiking? Take a look at this dilemma.

Kelly and the other hikers are trying to divide up all of the things that they need for their trip. The group wants the division of items to be equitable so that each person carries the same amount. If there are seven hikers, how can they figure this out? The group isn't sure how many items will need to be carried.

Is there a way to write a variable expression to figure this out?

**This Concept will show you how to write a variable expression for this dilemma.**

### Guidance

Previously we learned how to evaluate expressions, both alone and in relation to real-world problems. We can use some familiar situations to write and evaluate our own variable expressions. The key to writing variable expressions is analyzing the information you have, identifying the information you need, and recognizing the terms that indicate which mathematical operation to use.

**Let’s imagine that Ralph is a baker who makes \begin{align*}l\end{align*} number of loaves of bread each day.**

- If he uses 5 cups of flour for each loaf, the total amount of flour he uses each day would be represented as \begin{align*}5l\end{align*}.
- If he only sells half the loaves he makes, then he sells \begin{align*}\frac{l}{2}\end{align*}.
- In 2 days, 3 days, 4 days, Ralph would make \begin{align*}2l, 3l\end{align*}, and \begin{align*}4l\end{align*} loaves of bread.

Now it's time for you to try a few on your own. Write variable expressions for each real-world problem.

#### Example A

Karen bakes cookies every day. How many total cookies would she bake in seven days?

**Solution: \begin{align*}7c\end{align*}**

#### Example B

Eden caught fourteen fish and ate some.

**Solution: \begin{align*}14 - x\end{align*}**

#### Example C

Jessica read a few books each week. How many did she read over four weeks?

**Solution: \begin{align*}4x\end{align*}**

Here is the original problem once again.

Kelly and the other hikers are trying to divide up all of the things that they need for their trip. The group wants the division of items to be equitable so that each person carries the same amount. If there are seven hikers, how can they figure this out? The group isn't sure how many items will need to be carried.

Is there a way to write a variable expression to figure this out?

We can write a variable expression to figure out how many items each person will carry.

First, think about the variable. The unknown quantity is the number of items. Let's call that \begin{align*}x\end{align*}.

There are seven people to carry these items.

We can divide the total number of items by 7.

Here is our answer.

**\begin{align*}\frac{x}{7}\end{align*}**

### Vocabulary

- Algebraic Expression
- an expression that contains numbers, variables and operations.

- Variable
- a letter used to represent an unknown quantity.

- Variable Expression
- an algebraic expression that contains one or more variables.

### Guided Practice

Here is one for you to try on your own.

Write a variable expression to express the following situation.

John runs every day. The number of miles that he runs varies per day. Sometimes he runs four miles and sometimes two miles. Write a variable expression to show John's total miles for three days.

**Answer**

The number of miles that John runs per day is our variable. That is an amount that changes. We can call that \begin{align*}m\end{align*}.

We want the total miles for three days.

**Our answer is \begin{align*}3m\end{align*}.**

### Video Review

Khan Academy Writing Variable Expressions

### Practice

Directions: Use what you learned about variables and real-life situations for the next problems. Choose a variable to represent the number and write an algebraic expression for the following phrases.

1. 19 decreased by a number

2. 4 less than the product of 4 and a number

3. 30 more than a number

4. 12 more than 3 times a number

5. A number divided by seven

6. A number and seven divided by two

7. 16 times an unknown number

8. A number divided by eight

9. The quantity of a number and seven times two

10. The quantity of a number and five divided by five

11. 22 decreased by a number

12. Seventeen less than three times a number

Directions: Now solve each problem using variable expressions.

13. A librarian has 4 times as many mystery books as romances. She lends out 12 mysteries. How many mysteries does she have now if she started with 15 romances?

14. In Saturday’s basketball game, Roman scored a fourth of his teams points. If the team scored 48 points total, how many points did Roman score? Write an expression and solve.

15. At the garden show daffodil bulbs cost $3 and tulip bulbs cost $4. Latoya buys 7 tulip bulbs and twice as many daffodil bulbs as tulips bulbs. How much does she spend total? Write an expression and solve.