Coach Taylor is driving the middle school track team to a district competition. The 26 team members suggest that the coach allow the school’s pep squad to travel with them to the competition to cheer them on. Coach Taylor likes the idea and has to choose between two buses to transport the track team and the 27 students on the pep squad. One bus has a 58-passenger capacity and the other bus’ capacity is 42. How can Coach Taylor use this information to determine how many seats will be left on each bus for the pep squad?

In this concept, you will learn how to write addition and subtraction phrases as single variable expressions.

### Writing Addition and Subtraction Phrases as Expressions

A **variable** is a letter used to represent an unknown quality. An **expression** is a combination of variables, numbers and operations without an equal sign. Because expressions do not contain equal signs, they are evaluated instead of solved. When an expression contains a variable representing an unknown number, it is referred to as a **variable** **expression**.

For example, variable expression.

is aVariables in an expression can have different values. The variable in the expression, \begin{align*}x\end{align*}

Evaluate the following expression.

\begin{align*}3x+1\end{align*}

First, substitute “4” for the variable “

”.\begin{align*}3(4)+1\end{align*}

Next, follow the order of operations and multiply 3 and 4.

\begin{align*}12 + 1\end{align*}

Then, add 12 and 1.

13

The answer is 13.

Here, the expression was given to you. There will be times when you may have to write an expression from a phrase or situation.

Expressions can be written to represent different situations. When writing expressions, pay attention to key words which identify different operations, unknown variables and numbers. After identifying key words, you can write an expression to symbolize the situation as a mathematical expression.

Here are some key words that indicate addition and subtraction.

Addition:

- Sum
- Plus
- Altogether
- And

Subtraction:

- Difference
- Less than
- Take away

Find the key words in this phrase then write the phrase as an expression.

Nine less than an unknown quantity

First, look for the numbers in the phrase. The only number in the phrase is nine (9).

9

Next, identify the key words in this phrase.

“Less than” indicates subtraction.

Then, there are the words “unknown quantity” which can be represented by a variable. Let‘s use the variable “

”.

Now you can rewrite the phrase.

9 less than

Since 9 is subtracted from

, the expression is written as .The answer is

.### Examples

#### Example 1

Earlier, you were given a problem about the track team’s district meet.

Coach Taylor will be driving 26 members of the track team to a district meet. He has to determine which bus will have enough seats left to take the 27 students on the pep squad - the 42-passenger bus or the larger 58-passenger bus.

How can you write an expression to expression to represent this situation?

First, identify the key numbers.

There are 26 members on the track team and 27 students on the pep squad.

Next, identify the key words and operations.

“left” indicates “subtraction”

Then, identify the unknown number. The unknown is which bus the team will use, so let the total number of seats on the bus Coach Taylor chooses be represented by the variable “

.

Now, write the expression.

You can evaluate the expression if the team uses the 58-passenger bus by substituting 58 for “

” in the expression.\begin{align*}\begin{array}{rcl}
&& x -26 \\
&& 58-26 \\
&& 32
\end{array}\end{align*}

There will be 32 seats left for the pep squad.

You can also evaluate the expression if the team uses the 42-passenger bus by substituting 42 for “

” in the expression.\begin{align*}\begin{array}{rcl}
&& x -26 \\
&& 42-26 \\
&& 16
\end{array}\end{align*}

There will be 16 seats left for the pep squad.

The answer is Coach Taylor should choose the 58-passenger bus. It will have 32 seats left to take the 27 members of the pep squad.

#### Example 2

Write the phrase as an expression: an unknown number and four.

First, identify the number in the phrase.

4

Next, identify the key words and operations.

“and” means “add”

Then, substitute a variable for the “unknown number”. Let

represent the unknown number.\begin{align*}x\end{align*}

The answer is

.#### Example 3

Write the phrase as an expression: the difference between ten and an unknown number.

First, identify the number in the phrase.

10

Next, identify the key words and operation.

“difference” means “subtraction”

\begin{align*}-\end{align*}

Then, substitute a variable for the “unknown number”. Let

represent the unknown number.

As the phrase does not identify whether 10 is being subtracted from the unknown number or the unknown number is subtracted from ten, there are two possible expressions for this phrase.

\begin{align*}10 - x\end{align*}

The answer is \begin{align*}x - 10\end{align*}

#### Example 4

Write the phrase as an expression: seven less than a number.

First, identify the number in the phrase.

7

Next, identify the key words and operation.

“less than” means “subtraction”

Then, substitute a variable for the “unknown number”. Let

represent the unknown number.

In this example, the phrase specifically states that 7 is being subtracted from the unknown number.

The answer is

.#### Example 5

Write the phrase as an expression: seven less than the quantity of six and an unknown number.

This phrase has both addition and subtraction in it. The key here is the word “quantity”. This lets you know that there is going to be a set of parentheses in the expression.

Begin by writing the part of the phrase inside the parentheses first.

The quantity is six and an unknown number.

First, identify the number in the parentheses.

6

Next, identify the key words and operation inside the parentheses.

“and” means “add”

Then, substitute a variable for the unknown number. Let \begin{align*}x\end{align*} represent the unknown number.

Now, rewrite the original phrase with the expression inside the parentheses and follow the same steps.

Seven less than

First, identify the numbers in the phrase.

7

Next, identify the key words and operation.

“less than” means “subtract”

Then, identify the quantity that 7 is being subtracted from.

\begin{align*}(6+x)\end{align*}

The answer is

### Review

Write the following addition and subtraction phrases as single-variable expressions.

- The sum of six and an unknown number
- A number and seven
- Four less than a number
- The sum of a number and fourteen
- The difference between twenty and an unknown number
- Twenty-five take away a number
- Ten less than a number
- Thirty-seven plus an unknown quantity
- The sum of nine and an unknown number
- An unknown number and eight
- An unknown number plus the quantity six plus seven.
- The sum of fifteen and an unknown number
- Thirty less than the quantity of twenty - five and an unknown number.
- Twelve less than an unknown number
- Sixteen and seven plus an unknown number

### Review (Answers)

To see the Review answers, open this PDF file and look for section 12.1.

### Resources