Question 574533: The product of digit of two digit number is 24.If 18 is added to the number digits are reversed.find the number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The product of digit of two digit number is 24.
If 18 is added to the number of digits are reversed. find the number.
:
Let x = the 10's digit
Let y = the units
then
10x + y = the number
:
"The product of digit of two digit number is 24."
x * y = 24
:
"If 18 is added to the number, digits are reversed."
10x + y + 18 = 10y + x
10x - x + 18 = 10y - y
9x + 18 = 9y
simplify, divide by 9. results
x + 2 = y
:
Using the 1st equation, replace y with (x+2)
x(x+2) = 24
x^2 + 2x - 24 = 0; our old friend, the quadratic equation!
Factors to
(x+6)(x-4) = 0
the positive solution
x = 4
then
y = 4 + 2
y = 6
:
46 is the number
:
:
Check this: 46 + 18 = 64, the number reversed
:
The solution, x=-6 will also work, check it out.
-64 is the number,
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