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Sum of the digits of a two digit number is 14. If we add 18 to the original number, the digits interchange their places. Write two equations for these two statements.
 
 

Asked by Shivansh 17th March 2017, 4:04 PM
Answered by Expert
Answer:

begin mathsize 14px style Let space the space digit space at space the space ten apostrophe straight s space place space be space straight x space and space the space digit space at space the space unit apostrophe straight s space place space be space straight y.
Sum space of space the space digits space is space 14.
rightwards double arrow straight x plus straight y equals 14
Original space number equals xy space equals space 10 straight x plus straight y
Number space after space reversing space the space digits equals yx equals 10 straight y plus straight x
According space to space question comma
10 straight x plus straight y plus 18 equals 10 straight y plus straight x
rightwards double arrow 10 straight x minus straight x plus straight y minus 10 straight y equals negative 18
rightwards double arrow 9 straight x minus 9 straight y equals negative 18
rightwards double arrow 9 left parenthesis straight x minus straight y right parenthesis equals negative 18
straight x minus straight y equals negative 2
Thus comma space the space two space equations space are space
straight x plus straight y equals 14 space and space straight x minus straight y equals negative 2 end stylebegin mathsize 14px style Let space the space digit space at space the space ten apostrophe straight s space place space be space straight x space and space the space digit space at space the space unit apostrophe straight s space place space be space straight y.
Sum space of space the space digits space is space 14.
rightwards double arrow straight x plus straight y equals 14
Original space number equals xy space equals space 10 straight x plus straight y
Number space after space reversing space the space digits equals yx equals 10 straight y plus straight x
According space to space question comma
10 straight x plus straight y plus 18 equals 10 straight y plus straight x
rightwards double arrow 10 straight x minus straight x plus straight y minus 10 straight y equals negative 18
rightwards double arrow 9 straight x minus 9 straight y equals negative 18
rightwards double arrow 9 left parenthesis straight x minus straight y right parenthesis equals negative 18
straight x minus straight y equals negative 2
Thus comma space the space two space equations space are space
straight x plus straight y equals 14 space and space straight x minus straight y equals negative 2 end style

Answered by Expert 17th March 2017, 4:19 PM
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