Bucket has 4 types of balls: small white small black large white large black. Ratio small:large is 3:7. Ratio white:black is 5:7. Jack says "There must be at least 60 balls in the bucket." Is Jack correct? Show working to justify your answer
2 Answers
No.
Explanation:
Four Types of balls:
- Small White
- Small Black
- Large White
- Large Black
Small Has
So
Yes
Explanation:
If the small:large ratio is
then for some integer
That is, in total, there must be
Similarly:
If the white:black ratio is
then for some integer
That is, in total, there must be
The total number of balls must be
The smallest such number is the Least Common Multiple of
Since