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When you reverse the digits of your 2 digit number the new number is 45 less than the original number and the sum of the two digits times the difference of the two digits is 45 What are the two digit?
Wiki User
∙ 13y ago
72 is the original number
72 - 27 = 45
(7+2)*(7-2) = 9*5 = 45
Here's how to do it via algebra:
Choose x as ten's & y as the one's digit of your number.
So your original number is 10x+y
When you reverse the digits of the number the new number (10y+x) is 45 less than the original so:
10y+x =10x+y-45
10y-10y+x-x =10x-x+y-10y-45+45 (rearrange)
9x-9y=45 (you can simplify by dividing by 9)
x-y =5 [1st equation]
Next the sum of the digits times the difference of the digits is 45 so we have this equation:
(x+y)*(x-y)=45 [2nd equation]
Now we have 2 equations with 2 unknowns. From the first equation : (x-y)= 5 we can substitute that value into the 2nd equation, so:
(x+y)*(5)=45
(x+y) =9 [3rd equation]
Now using the 3rd equation and the 1st equation we can solve for x & y.
x-y= 5
x+y=9
--------------- (add the 2 equations)
2x =14
x= 7
Substitute 7 into either equation above to solve for y.
(7) + y=9
y= 9 - 7 = 2
So the tens digit is 7 & ones digit is 2 hence 72 is the original number.
Wiki User
∙ 13y ago
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