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Videos, worksheets, solutions, and activities to help Algebra students learn how to solve digit word problems.

Sum of Digits

How to solve a problem when asked to switch the digits of a 2-digit number.

Example: The sum of the digits of a two-digit counting number is 5. When the digits are reversed, the number is 9 greater than the original number. What was the original number?

Students learn to solve digit word problems using a system of linear equations, as demonstrated in the following problem.

Example: The sum of the digits of a two-digit number is 7. The value of the number is 2 less than 12 times the tens digit. Find the number.

The two variables used in this problem are t, the tens digit, and u, the units digit. Since the sum of the digits of the two-digit number is 7, one equation is t + u = 7. Since the value of the number is 2 less than 12 times the tens digit, the other equation is 10t + u = 12t -- 2. Note that 10t + u is used to represent "the value of the number".

Examples:

(1) The sum of the digits of a 2-digit number is 10. The tens digit is 4 times the ones digit. Find the number.

(2) A 2-digit number is 10 times the sum of its digits. The tens digit is 2 greater than the units digit. Find the number.

(3) The sum of the digits of a 2-digit number is 14. If 18 is added to the number, the result is the number with its digits reversed. Find the original number.

(4) The sum of the digits of a 2 digit number is 9. If the digits are reversed, the new number is 9 less than 3 times the original number. Find the original number.

Example: The sum of the digits of a two-digit counting number is 5. When the digits are reversed, the number is 9 greater than the original number. What was the original number?

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