Representing a situation or solving a problem symbolically means doing so using an abstract representation.

The number 13 is a representation for thirteen of any object. It can represent 13 apples, 13 blocks of concrete, 13 houses, etc.  

At no time are any actual "concrete" thirteen or eight objects used to represent the situation, nor are there pictorial representations of objects. 13, 8 and 13 + 8 = 21 are symbolic representations leading to the conclusion that:

• Thirteen apples plus eight apples results in a total of twenty-one apples.
• Thirteen blocks of concrete plus eight blocks of concrete results in a total of twenty-one blocks of concrete.
• Thirteen houses plus eight houses results in a total of twenty-one houses.

And so on.       (Learn Alberta)

An equation is a statement showing that two mathematical expressions are equal. (Learn Alberta)

A variable is a symbol used to represent:

• a number in an expression
• an unknown value in an equation
• a number or element of a set in a relation connecting two or more sets

(Learn Alberta)