A bag contains a total of 16 golf balls, 6 of which are white. A golfer wants to add 112 golf balls to the bag. He wants the ratio of white to striped golf balls to remain the same. How many of each should he add? Show your work.
Let's assume that the number of striped golf balls in the bag is W
So the total number of golf balls in the bag is 16+W
The ratio of white to striped golf balls in the bag is 6/W
Since the golfer wants to maintain the same ratio after adding 112 golf balls, the ratio will become 6/(W+112)
The equation to represent the ratio is 6/W = 6/(W+112)
To eliminate the fractions, we can cross multiply:
6(W+112) = 6W
6W + 672 = 6W
672 = 6W - 6W
672 = 0W
Since 0W = 672 is a contradiction, it means there's no solution for the equation.
Therefore, the golfer cannot add any golf balls to maintain the same ratio.