Math CentralQuandaries & Queries


Question from daphne, a student:

im a 2-digit number less than 85.the sum of my digits is 9. the number in my ones place is twice my tens digit. who am i?

We have two responses for you

Without algebra: Make up a list of two digit numbers where the number in the ones place is twice the tens digit. It will start 12, 24,...
Now check the sums of digits.

Using simple algebra:

Let the digits be A and B.

The first of the two conditions above can be written symbolically as

A + B = 9

Do the same thing for the other condition.

Then use one of the two equations to substitute something involving "A" for the "B" in the other one.

You then have an equation with only "A" in it that you should be able to solve.

By the way - did you notice that we never used the "less than 85" bit? I wonder why it was included?

Good hunting!



My technique is similar to RD's "without algebra" method but I would list the possibilities differently. The tens digit can be 1 to 9 so start with 1. If the tens digit is 1 and the sum of the digits is 9 then the units digit is 8, Does 18 satisfy the condition that the ones digit is twice the tens digit? Next try the tens digit being 2 and so on.


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