# math

A positive two-digits number is such that the product of the digits is 24.When the digits are reversed,the number formed is greater than the original number by 18.Find the number

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1. let the unit digit be x
and the tens digit by y
then the original number is 10y + x
and the number reversed is 10x + y

10x + y - (10y + x) = 18
9x - 9y = 18
x - y = 2
but we also know that xy = 24

it should be obvious that the two number are 6 and 4.
Since reversing the numbers made the number bigger, the original must have been 46

check:
6x4 = 24 , that's good
original = 46
reversed = 64
64 - 46 = 18 , all is good!

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2. Let the digits be xy,x is the ones digit& y tens digit.Hence;
Xy=24---(i)
(X+10y)-(y+10x)=24---(ii)
(ii)
X+10y-y-10x
X-10x+10y-y
-9x+9y=18
9y-9x=18
Y-x=2--(ii)
but;xy=24
X=2+y
Y(2+y)=24
Y'2+2y-24=0
Product=-24
Sum=2
Numbers 6,-4
Since digits were(+)ignore the(-)sign
Product of digits xy;6×4=24,terrific
Therefore;
Original number=46
New number=64

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