SOLUTION: The difference of the digits of a two-digit number is 4. Find the number if the product of the digits is 45.

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Question 527452: The difference of the digits of a two-digit number is 4. Find the number if the product of the digits is 45.
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Let our answer be in the form 10x + y. We'll use this later.
x-y = 4 --> x = 4+y
xy = 45
(4+y)y = 45
4y + y^2 = 45
y^2 + 4y -45 = 0
(y+9)(y-5) = 0
This gives us answers of y=-9 and y=5. Since a negative answer won't give us the answer we're looking for, then y = 5 is the only logical solution.
Plug y = 5 back into either equation.
x(5) = 45
5x = 45
x = 9
Going back to our 10x+y...
10(9) + 5 = 95
Thus our answer is 95.