### Writing Equations

An equation is a number sentence stating that two expressions have the same value. The difference between an expression and an equation is the equal sign, $=$. If a problem is stated verbally, the first step in solving is to translate the description of the problem into an algebraic equation.

Some words and phrases that represent the equal sign $=$ include:

- Amounts to
- Equals
- Gives
- Is
- Is the same as
- Represents
- Yields

To translate a problem description into an equation, look for the word or phrase that represents the equal sign. Determine what part of the problem describes the expression on each side. Translate the two expressions, and place the equal sign between them.

### Writing Algebraic Equations

Description | Equation |
---|---|

$\text{{\color{#c42126}{The sum of a number and 32}}}$ is ${\color{#0047af}{54}}$. |
${\color{#c42126}{n+32}}={\color{#0047af}{54}}$ |

$\text{{\color{#c42126}{The cost of 5 pounds of bananas}}}$ is ${\color{#0047af}{\$3.25}}$. |
${\color{#c42126}{5p}}={\color{#0047af}{3.25}}$ |

$\text{{\color{#c42126}{Gabriela has earned 117 credit hours, which}}}$ is $\text{{\color{#0047af}{3 fewer than the number of credits she needs to graduate}}}$. |
${\color{#c42126}{117}}={\color{#0047af}{c-3}}$ |

A library has 86 science fiction paperbacks and e-books combined. The number of paperbacks are 4 fewer than twice the number of e-books.

Write an equation that represents the combined number of science fiction paperbacks and e-books.

Choose a variable.

The number of paperbacks is described in relation to the number of e-books. So, let $x$ represent the number of e-books:*twice the number*means to multiply by 2, or $2x$. The phrase

*4 fewer*means to subtract 4. So, the number of paperbacks is:

*has*represents the equal sign. The word

*combined*represents addition. So, add the expressions that represent the number of paperbacks and e-books:

### Application of Equations

#### Geometric Formulas

Write the values using the appropriate units of measure.

The perimeter is 46 cm.

The area is 120 square centimeters.

Eve opens an account with $100. The account earns 6% interest compounded monthly. How much will be in the account after 5 years?

Use the formula for compounded interest, or interest that is added back into the amount that earns interest.The original amount in the account is $100, or $P$.

The rate, $r$, of 6% expressed as a decimal is 0.06.

The time, $t$, is years.