In the problem, the age of Bob and Mary are being compared to Sue's age. So let x be the age of Sue. Then, express in math form the given conditions.

For the condition "Bob is twice Sue's age", its math form is 2x.

And the condition "Mary is one year younger than Sue", its math form is x-1.

So the expressions that represent the ages of each person are:

Sue's age `= x`

Bob's age `= 2x`

Mary's age `= x - 1`

To set-up the equation, refer to the first condition "The sum of Bob, Mary and Sue's age is 59".

So, the equation is:

`x + 2x + (x - 1) = 59`

Simplifying the right side, it becomes:

`4x - 1 = 59`

Isolating the x, yields:

`4x=60`

`x=15`

Then, plug-in the value of x to the expression that represents the age of Bob and Mary.

Bob's age `= 2(15)=30`

Mary's age `= 15-1=14`

**Thus, Mary is 14 years old, Sue is 15 years old, and Bob is 30 years old.**