In a chess club there are x boys and y girls. If ten more boys join and one more girl joins, there is an equal amount of boys and girls. Knowing that y = 2x+2, Calculate x and y. [4 marks]
There are x boys and y girls. So x = boys, y = girls. Ten boys join so x + 10 = boys, one girl joins so y + 1 = girls. These values are said to be equal, so we construct an equation with x and y. x + 10 = y + 1. We want to isolate y, so taking 1 to the other side gives y = x + 9. This is our first equation. We are also told an equation relating the two is y = 2x + 2, this is our second equation. We then form a simultaneous equation to solve for x and y: (1) y = x + 9 (2) y = 2x +2 Making the (1) and (2) equal each other we get: x + 9 = 2x + 2, 9 - 2 = 2x - x, x = 7 We then sub in x + 7 into one of the equations (choosing (1) as its the simplest) to get: y = 7 + 9, y = 16
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