Math CentralQuandaries & Queries


Question from jhoanna, a student:

the sum of the digits of a two digit number is 10. The value of the number is 16 times the units digit. Find the number.

Hi Jhoanna,

I can see two ways to approach this problem. I suggest you try both to see if the answers you get agree.

The most direct method is to first write down all two digit numbers which have 10 as the sum of their digits. There are not very any

and so on.

Now check each one to see if the number is 16 times its units digit.

The second method is to use algebra. If the number has units digit $b$ and tens digit $a$ then the number is $10 a + b.$

Now write two equations

  • the sum of the digits, $a$ and $b$ is 10, and

  • the number is 16 times its units digit $b.$

Solve the equations for $a$ and $b.$

I hope this helps,

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