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# Expressions for Real-Life Situations

## Using real-life, practical situations, we look at applications of algebra by developing algebraic expressions for real world situations. Learn more.

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Expressions for Real-Life Situations

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 l\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 5l\begin{align*}5l\end{align*}.
• If he only sells half the loaves he makes, then he sells l2\begin{align*}\frac{l}{2}\end{align*}.
• In 2 days, 3 days, 4 days, Ralph would make 2l,3l\begin{align*}2l, 3l\end{align*}, and 4l\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: 7c\begin{align*}7c\end{align*}

#### Example B

Eden caught fourteen fish and ate some.

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

#### Example C

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

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

There are seven people to carry these items.

We can divide the total number of items by 7.

x7\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.

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

We want the total miles for three days.

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

### 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.

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

TermDefinition
Algebraic Expression An expression that has numbers, operations and variables, but no equals sign.
Variable A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n.
The content structure of the given text is a brief introduction to the topic of writing variable expressions for real-life situations, followed by a specific example of hikers trying to divide items equitably.

Analysis:
single_question_with_answer

the text contains a mathematical question embedded within a real-life scenario (dividing items among hikers) and provides an answer in the form of a variable expression (x/7).
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
You are viewing an older version of this Concept. Go to the latest version.

# Expressions for Real-Life Situations

## Using real-life, practical situations, we look at applications of algebra by developing algebraic expressions for real world situations. Learn more.

Estimated6 minsto complete
%
Progress
Practice Expressions for Real-Life Situations

MEMORY METER
This indicates how strong in your memory this concept is
Progress
Estimated6 minsto complete
%
Expressions for Real-Life Situations

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 l\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 5l\begin{align*}5l\end{align*}.
• If he only sells half the loaves he makes, then he sells l2\begin{align*}\frac{l}{2}\end{align*}.
• In 2 days, 3 days, 4 days, Ralph would make 2l,3l\begin{align*}2l, 3l\end{align*}, and 4l\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: 7c\begin{align*}7c\end{align*}

#### Example B

Eden caught fourteen fish and ate some.

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

#### Example C

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

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

There are seven people to carry these items.

We can divide the total number of items by 7.

x7\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.

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

We want the total miles for three days.

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

### 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.

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

TermDefinition
Algebraic Expression An expression that has numbers, operations and variables, but no equals sign.
Variable A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n.
user
The content structure of the given text is a brief introduction to the topic of writing variable expressions for real-life situations, followed by a specific example of hikers trying to divide items equitably.

Analysis:
TYPE: SINGLE_QUESTION_WITH_ANSWER

The text contains a mathematical question embedded within a real-life scenario (dividing items among hikers) and provides an answer in the form of a variable expression (x/7).