### Concept (1)

One difficult type of Algebra problem are word problems asking about the sum of digits in a two digit number. Solving systems of equations by substitution is one of the most common ways to solve sum of digits problems. Other types of word problems using systems of equations include mixture problems, money word problems, work word problems and rate word problems.

### Sample Problems (3)

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The sum of the digits of a 2-digit number is 12. When the digits are reversed, the new number is 54 more than the original number.

What is the original number?
###### Problem 1
How to solve a problem when asked to switch the digits of a 2-digit number and the result is more than the original.

The sum of the digits of a certain 2-digit number is 6. When you reverse the digits, you decrese the number by 54.

Find the number.
###### Problem 2
How to solve a problem when asked to switch the digits of a 2-digit number and one digit is zero.
###### Problem 3
Writing a system of equations and solving word problems involving switched digits from a single number