I am a 2 digit number. if sum of my two digits is added to the product of my digits, it is me again. can you find me?
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Step-by-step explanation:
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.
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