Archive
17th of March 2017
Mathematics
Q:


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.



Shivansh Srinet - CBSE - Class IX

Friday, March 17, 2017 at 16:04:PM

A:

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

Friday, March 17, 2017 at 16:19:PM