### Translating Words into Numbers

To solve word problems, you must be able to translate words into mathematical operations. You must analyze the language of the question and determine what the question is asking you to do.

The following list presents phrases commonly found in word problems along with their mathematical equivalents:

■ A **number** means a **variable**.

Example

17 minus a number equals 4.

17 – x = 4

■ **Increase** means **add**.

Example

a number increased by 8

x + 8

■ **More than** means **add **.

Example

4 more than a number

4 + x

■ **Less than** means **subtract**.

Example

8 less than a number

x - 8

■ **Times** means **multiply**.

Example

6 times a number

6x

■ **Times the sum** means to **multiply a number by a quantity**.

Example

7 times the sum of a number and 2

7(x+2)

■ Note that variables can be used together.

Example

A number y exceeds 3 times a number x by 12.

y = 3x + 12

exceed [ɪk’siːd] превышать. Дословно: переменная у превышает 3х на 12.

■ **Greater than** means **>** and **less than** means **<**.

Examples

The product of 10 and х is greater than 15.

10x > 15

When 1 is added to a number x, the sum is less than 29.

x + 1 < 29
■ **At least** means **≥** and **at most** means **≤**.

Examples

The sum of a number x and 5 is at least 11.

x + 5 ≥ 11

When 14 is subtracted from a number x, the difference is at most 6.

x - 14 ≤ 6

■ To **square** means to use an **exponent of 2.**

Example

The square of the sum of m and n is 25.

*Practice Question*

If squaring the sum of y and 23 gives a result that is 4 less than 5 times y, which of the following equations could you use to find the possible values of y?

*Answer*

Break the problem into pieces while translating into mathematics:

*squaring* translates *to raise something to a power of 2*

*the sum of y and 23* translates to .

So, *squaring the sum of y and 23* translates to

gives a result translates to

*4 less than* translates to

*5 times y* translates to .

So, *4 less than 5 times y* means .

Therefore, *squaring the sum of y and 23 gives a result that is 4 less than 5 times y* translates to:

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