SOLUTION: Two digit number is such that the product of their digits is 12.when the digits are reversed, the number formed exceeds the original by 9.find the original number
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Question 1023919: Two digit number is such that the product of their digits is 12.when the digits are reversed, the number formed exceeds the original by 9.find the original number Found 2 solutions by fractalier, solver91311:Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website! Call the number x in the tens place and y in the ones place. We can then write
xy = 12
and
10y + x = 10x + y + 9 or
9y - 9x = 9 or
y - x = 1
y = x + 1
Now substitute that into the first equation and get
x(x+1) = 12
x^2 + x - 12 = 0
(x + 4)(x - 3) = 0
x = 3
The number must be 34.
If you reverse the digits of a two-digit number and get a number that differs from the original by 9, then the difference between the two digits must be 1. (If the two numbers differ by 18, then the difference between the two digits is 2, and so on).
So you need to find two single digits that differ by 1 where the product of the digits is 12.
Solve the quadratic.
John
My calculator said it, I believe it, that settles it
