BRAIN TEASERS
Fantastic Fractions
Start with some white sand in a bucket. Add one scoop of a well-mixed blue/red mixture to the bucket, and the overall mixture in the bucket is 1/8 red. Add four more scoops of the blue/red mixture, and the bucket becomes 2/5 red.
What fraction of the blue/red mixture is red?
Answer:
8/9
Solution:
Let x be fraction of red in the mixture. After one scoop has been added, the ratio of the red to total is x:8x.
After four more scoops, the ratio is 5x:(8x+4).
This ratio is equivalent to 2/5, so we solve the proportion 5x/(8x+4) = 2/5.
Therefore, 25x = 16x + 8, so 9x = 8 or x = 8/9.