Question

There are 100 balls in a bag.
The balls are red, blue, green or white.
The ratio of blue to red is 5: 1
There are twice as many blue as green.
1 of the balls are green.
How many white balls are in the bag?​

Answer 1

Answer:

There are 100 balls in a bag.

The balls are red, blue, green or white.

The ratio of blue to red is 5: 1

There are twice as many blue as green.

1 of the balls are green.

How many white balls are in the bag?

Step-by-step explanation:

There are twelve different answers to this question. Here are some things to notice:

Because of the ratio 3:5

Red must be a multiple of 3

Green must be a multiple of 5

Because of the ratio 1:3

Blue must be a multiple of 3

Here is how I solved the problem and found all twelve answers:

Pick any multiple of 3 between 3 and 36

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 or 36

This is the number of Red balls

Divide Red by three then multiply by five

This is the number of Green balls

Subtract the Red and Green numbers from 100

This tells you how many balls are Blue and Yellow

Divide that difference by four

This tells you the number of Yellow balls

Multiply Yellow by three

This tells you the number of Blue balls

Be sure to double-check your ratios

Let’s do that with the biggest possible number of red balls:

Start with 36 Red balls

36 ÷ 3 × 5 = 60 Green Balls

100 – 36 – 60 = 4 balls left

4 ÷ 4 = 1 Yellow Ball

1 × 3 = 3 Blue Balls

36:60 → 3:5 ← correct

1:3 ← correct

Let’s do that again, starting with the smallest number of balls:

Start with 3 Red balls

36 ÷ 3 × 5 = 5 Green Balls

100 – 3 – 5 = 92 balls left

92 ÷ 4 = 23 Yellow Balls

23 × 3 = 69 Blue Balls

3:5 ← correct

23:69 → 1:3 ← correct

Can you find the other ten answers

start with 6 red balls, 9 red balls, 12 red balls, etc.