Math CentralQuandaries & Queries


Question from Christine, a student:

Five times the sum of the digits of a two digit number equals the number. If the digits are reversed, it becomes nine more than the original number. What is the original number?
I really don't understand this question, help me please

Hi Christine,

Suppose that the tens digit of the number is a and the units digit is b, then the number is 10a + b. The sum of the digits is a + b and five time this quantity is the number itself. Hence

5(a + b) = 10a + b.

Use the second sentence in your problem to write another equation in a and b and then solve the two equations for a and b. Make sure you check your answer.


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