A box has balls, each either white or black, there being as many metallic white balls as metallic black balls. If of the white balls and of the black balls are metallic, then the number of non-metallic balls in the box is
A box has balls, each either white or black, there being as many metallic white balls as metallic black balls. If of the white balls and of the black balls are metallic, then the number of non-metallic balls in the box is
Entered answer:
Solution
We have 450 balls total, each either white or black. The key insight is that metallic white balls = metallic black balls. We call this number .
We say there are metallic white balls and metallic black balls.
If 40% of white balls are metallic, then metallic white balls = 0.4 × (total white balls)
If 50% of black balls are metallic, then metallic black balls = 0.5 × (total black balls)
Since metallic white balls = :
0.4 × (total white balls) =
Therefore: total white balls =
Since metallic black balls = :
0.5 × (total black balls) =
Therefore: total black balls =
Total balls = White balls + Black balls = 450
Now we know:
Total white balls =
Total black balls =
Metallic white balls = 100
Metallic black balls = 100
Non-metallic balls:
Non-metallic white =
Non-metallic black =
Total non-metallic balls =
Answer: 250