To solve this problem, we need to determine the percentage of red counters in a bag where the number of red counters to blue counters is given in the ratio 2:3. Here is a step-by-step solution:
1. Understanding the Ratio:
- The ratio of red counters to blue counters is 2:3. This means for every 2 red counters, there are 3 blue counters.
2. Calculating the Total Number of Parts:
- To find the total number of parts (counters), we add the parts of red counters (2 parts) and the parts of blue counters (3 parts).
[tex]\[
\text{Total parts} = 2 + 3 = 5
\][/tex]
3. Determining the Fraction of Red Counters:
- The fraction of the red counters out of the total counters is the number of parts for red counters divided by the total number of parts.
[tex]\[
\text{Fraction of red counters} = \frac{2}{5}
\][/tex]
4. Converting the Fraction to Percentage:
- To find the percentage, we convert the fraction into a percentage by multiplying by 100.
[tex]\[
\text{Percentage of red counters} = \left( \frac{2}{5} \right) \times 100 = 40\%
\][/tex]
Thus, the percentage of counters in the bag that are red is [tex]\(40\%\)[/tex].
