Let's solve the problem step by step.

Part (a) Write down the ratio of blue to green to yellow counters in the bag.

Given ratios:

• Blue : Green = 3 : 2
• Green : Yellow = 2 : 5

First, let's express these ratios in terms of all three colors:

1. The ratio of Blue : Green is given as 3:2.
2. The ratio of Green : Yellow is given as 2:5.

Since the ratio of Green is the common part, we can combine these two ratios by ensuring the Green part is consistent across both ratios.

• From Blue : Green = 3 : 2, we have Blue : Green = 3 : 2.
• From Green : Yellow = 2 : 5, we also have Green : Yellow = 2 : 5.

The common Green ratio is 2, so we can directly combine them:

• Blue : Green : Yellow = 3 : 2 : 5.

So, the ratio of Blue to Green to Yellow counters in the bag is 3:2:5.

Part (b) What percentage of the beads are green?

To find the percentage of green counters, we first determine the total ratio parts:

• Total parts = 3 (Blue) + 2 (Green) + 5 (Yellow) = 10 parts.

The green counters make up 2 parts out of the total 10 parts.

Now, calculate the percentage:

$\text{Percentage of green counters} = \left(\frac{2}{10}\right) \times 100 = 20\%$

So, 20% of the counters are green.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. If there are 30 blue counters, how many yellow counters are there in the bag?
2. If the total number of counters in the bag is 50, how many of them are green?
3. If 20 more yellow counters are added to the bag, what will be the new ratio of blue to green to yellow?
4. If the ratio of yellow to green counters becomes 7:2, what will be the new ratio of blue to green to yellow?
5. If 10 counters are removed randomly, what is the probability that none of them are green?

Tip: When dealing with ratios involving three or more quantities, it's helpful to align them based on the common quantity to combine them properly.