SOLUTION: 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.

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Question 888027: 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 ?

Answer by MathTherapy(10556) About Me  (Show Source):
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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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