Question 983984

Let &nbsp;<B>x</B>&nbsp; and &nbsp;<B>y</B>&nbsp; be the numbers of pencils in the boxes &nbsp;<B>a</B>&nbsp; and &nbsp;<B>b</B>&nbsp; respectively.


Then you have two equations in two unknowns


x + y = 112, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and


x - {{{1/5}}}x = y + {{{1/5}}}x.


From the second equation


5x - x = 5y + x, &nbsp;&nbsp;&nbsp;&nbsp;or


3x = 5y. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)


From the first equation


3x + 3y = 336. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)


Now, replace &nbsp;3x&nbsp; in the equation &nbsp;(2)&nbsp; by &nbsp;5y, &nbsp;according to &nbsp;(1). &nbsp;You will get 


5y + 3y = 336, &nbsp;&nbsp;&nbsp;&nbsp;or


8y = 336, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;or


y = {{{336/8}}} = 42. 


Now, &nbsp;x = {{{5y/3}}} = {{{(5*42)/3}}} = {{{210/3}}} = {{{70}}}.


Hence, &nbsp;there were &nbsp;70&nbsp; pencils in the box &nbsp;<B>a</B>&nbsp; and &nbsp;42&nbsp; pencils in the box &nbsp;<B>b</B>.