### 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
Example
a number increased by 8
x + 8
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.
$(m+n)^2 =25$
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?
$a. (y+23)^2 =5y-4$
$b. y^2+23=5y-4$
$c. y^2+(23)^2=y(4-5)$
$d. y^2+(23)^2=5y-4$
$e. (y+23)^2=y(4-5)$
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 $y+23$.
So, squaring the sum of y and 23 translates to $(y+23)^2$
gives a result translates to $=$
4 less than translates to $something-4$
5 times y translates to $5y$.
So, 4 less than 5 times y means $5y-4$.
Therefore, squaring the sum of y and 23 gives a result that is 4 less than 5 times y translates to: $(y+23)^2 =5y-4$

Translating Words into Numbers