A bag contains straws of three different colour. 1\4 of the straws are blue. The ratio of the number of red straws to that of green straws is 2:3. What is the ratio of the number of blue straws to that of green straws?

To solve this problem, we need to understand the proportions of each color of straw in the bag.

1. We know that 1/4 of the straws are blue. This means that the remaining 3/4 of the straws are either red or green.

2. We also know that the ratio of red to green straws is 2:3. This means that for every 2 red straws, there are 3 green straws.

3. To find the ratio of blue to green straws, we first need to determine what fraction of the 3/4 of the straws that are not blue are green.

4. Since the ratio of red to green straws is 2:3, we can say that the 3/4 of the straws that are not blue are divided into 5 equal parts (2 parts red + 3 parts green).

5. Therefore, each part is equal to 3/4 ÷ 5 = 3/20 of the total number of straws.

6. Since there are 3 parts that are green, the fraction of green straws is 3 parts * 3/20 = 9/20.

7. The ratio of blue to green straws is therefore 1/4 : 9/20.

8. To simplify this ratio, we can convert both fractions to have the same denominator. The least common multiple of 4 and 20 is 20, so we convert 1/4 to 5/20.

9. Therefore, the ratio of blue to green straws is 5:9.