SOLUTION: A 2 digit number is 52 greater than the product of its digits. If the ten's digit is 4 larger than the unit's digit, find the number.

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Question 1111809: A 2 digit number is 52 greater than the product of its digits. If the ten's digit is 4 larger than the unit's digit, find the number.
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the units digit.


Then the tens digit is (x+4), and the number is  10*(x+4) + x.


We are given that  10*(x+4) + x = x*(x+4) + 52.


It is your quadratic equation to find x.


x^2 - 7x + 12 = 0.

(x-4)*(x-3) = 0.


The equation has two roots. Both satisfy the problem's condition.


So, there are two solutions.

At x= 3 the number is 73.   At  x= 4 the number is 84.


Answer.  There are two solutions:  73 and 84.

Solved.