Question

A two digit number is obtained by adding the sum of its digits to the product of the digits. How many such numbers are possible?

Answer 1

Answer:

the two digit number, let’s say, is xy.

Therefore the value of the number is 10x + y.

So therefore, 10x + y = xy + x + y

9x = xy

subtract xy from both sides to get:

9x - xy = 0

Factor out an x, to get

(9 - y)x = 0.

well obviously x can’t be zero, since x is the first digit and should be larger than 0.

However, therefore then (9 - y) should be 0, which means that y = 9.

So therefore, to satisfy the stipulations of this two digit number, the ones digit must be one, leaving 19, 29, 39, 49, 59, 69, 79, 89, 99

And that’s 9 numbers.

Step-by-step explanation:

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