There are white, yellow and black counters in a bag in the ratio 1:4:5There are 2 white counters.How many yellow counters are there?

1. Break Down the Problem

To find the number of yellow counters, we need to use the given ratio of the counters and relate it to the number of white counters.

2. Relevant Concepts

The ratio of white to yellow to black counters is given as $1:4:5$. This means for every 1 white counter, there are 4 yellow counters and 5 black counters.

Let:

• $x$ be the common multiple that scales the ratio.
• The number of white counters = $1x$
• The number of yellow counters = $4x$
• The number of black counters = $5x$

Given that the number of white counters is 2: $1x = 2$ From this, we can determine $x$.

3. Analysis and Detail

Now, solve for $x$: $x = 2$ Next, we can calculate the number of yellow counters: $\text{Number of yellow counters} = 4x = 4 \times 2 = 8$

4. Verify and Summarize

We verify if our calculations align with the given ratio. Since we have:

• White counters: $2$ (which corresponds to $1 \times 2$)
• Yellow counters: $8$ (which corresponds to $4 \times 2$)
• Black counters: $10$ (which corresponds to $5 \times 2$)

The ratio $2:8:10$ simplifies to $1:4:5$, confirming our initial ratio.

Final Answer

There are 8 yellow counters in the bag.