A variable is a representation of an unknown value.
Let.s take the first part of the problem: Susan is 5 years older than her sister.
We know that Susan is older than her sister, since she is 5 years older. However, we don't know their actual ages. Susan's age is dependent on her sisters age, because without knowing the sister's ages, we cannot figure out Susan's age.
So we can use the variable x to represent the sister's age.
x = the sister's age ----> independent
x + 5 = Susan's age ----> dependent on her sister's age
Since their ages add up to 51, we can use the defined variables to create an algebraic equation.
x + (x + 5) = 51
When we solve this equation, we can determine x.