# 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

#### Answer:

No.

#### Explanation:

Four Types of balls:

- Small White
- Small Black
- Large White
- Large Black

Small Has

So

#### Answer:

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