A number consists of two digits whose product is 8.if the digits are interchanged, the resulting number will exceed the original one by 18. find the number.
solution . let the digits be x and y
x*y= 8 but if y*x= original number +18
now this is the problem , if i put 8 instead of the original number the equation becomes y*x= 8+18 , y*x= 26 , x= 26/y
and if i put it in the other equation , 26/y*y=8 ! y gets cancelled ?
I prefer to name the TENS and UNITS digits, T and U, respectively
Therefore, TU = 8 ------ eq (i)
The number is: 10T + U, and the number when the digits are interchanged is: 10U + T
Note that the ORIGINAL number, 10T + U is SMALLER than the interchanged number. We now have:
10T + U + 18 = 10U + T
10T - T + U - 10U = - 18
9T - 9U = - 18
9(T - U) = 9(- 2)
T - U = - 2
T = U - 2 ------- eq (ii)
Solve the system to determine T, the TENS DIGIT and U, the UNITS DIGIT. Remember that these values
MUST be POSITIVE (> 0)
Then do a check!!
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