When solving problems it is sometimes necessary to translate words, a table of data, or a physical model into expressions. There are two types of expressions: variable and numerical. Variable expressions have at least one variable (sometimes called an unknown) in them. Numerical expressions involve only numbers. Here are examples of each

Here is a table of key words that indicate addition and subtraction.
Operation 
Verbal expressions (key words) 
Variable expression 
$\large~+$ 

$\large~n+3$ 
$\large~$ 

$\large~x12$ 
Example 1
To find Bill's age, begin by placing their ages in a table...
When Angela's age is...  Bill's age is... 
5  8 
6  9 
7  10 
12  
n  n+3 
Notice that Bill is always 3 years older than Angela. So when Angela is 12 years old Bill will be 15 years old.
When Angela is n years old, Bill will be (n+3) years old.
Example 2
Alan is 8 years old.
Example 3
EXPLORE!


Question 1 Two sticks are laid endtoend. Their combined length is 18 inches. The shorter stick is m inches long. What is the length of the longer stick? 
[show answer] 
Question 2 Let a, b, and c represent the three lengths of the three sides of a triangle. What is the perimeter of the triangle? 
[show answer] 
Question 3 If the initial temperature is d degrees how many degrees will it be if the temperature goes up 3 degrees? 
[show answer] 