Question 980978


Let &nbsp;<B>x</B>&nbsp; be the number of mangoes that John collected, 

and let &nbsp;<B>y</B>&nbsp; be the number of mangoes that Marie collected.


If Marie gives &nbsp;7&nbsp; mangoes to John, &nbsp;then Jon will have &nbsp;(x+7)&nbsp; mangoes and Marie will have &nbsp;(y-7)&nbsp; mangoes. According to the condition, 


x + 7 = 2(y-7). 


In opposite, &nbsp;if John gives &nbsp;7&nbsp; mangoes to Marie, &nbsp;then Marie will have &nbsp;(y+7)&nbsp; mangoes and John will have &nbsp;(x-7)&nbsp; mangoes. &nbsp;Again, according to the second condition, 


y + 7 = x - 7. 


Thus you get the system of two linear equations in two unknowns


{{{system(x + 7 = 2(y - 7),
y + 7 = x - 7)}}}.


To solve it, express y from the second equation

y = x - 14


and substitute it to the first equation


x + 7 = 2((x-14) - 7),


x + 7 = 2x - 28 - 14,

x = 7 + 14 + 28 = 49. 


Thus John collected &nbsp;49&nbsp; mangoes.


Marie collected &nbsp;y = x - 14 = 49 - 14 = 35 mangoes.