Question 1151451
x = number of sudoku competition players.
y = number of crossword competition players.
60 = number of participants in both competitions.


since the number of participants in both is included in the total of each, you have:


x + y - 60 = 225
x + y = 285
y = 2x
3x = 285
x = 95
y = 190


you have 95 people who competed in the sudoku competition and 190 who competed in the crossword competition.


of the 95 who competed in the sudoku competition, 60 also competed in the crossword competition.


therefore, you have:
35 who competed only in the sudoku competition.
130 who competed only in the crossword competition.
60 who competed in both.


total who competed in both competitions is 35 + 130 + 60 = 225


the question is how many competed in the sudoku competition.


that would be 35 + 60 = 95.


the basic assumption is that the number who competed in both are counted in the number who competed in each.


that means they are being double counted and so one of them needs to be subtracted out.


that's why you get x + y - 60 = 225.


that becomes your basic equation that you use to solve for x and y, taking nto account that y = 2x.