Final answer:
To find the simplest form of the ratio of juniors to adults in a horse riding club, we use proportional reasoning based on the given ratios of children juniors to adults (3:1) and juniors to children (2:5), identifying that 'children juniors' refers to 'juniors'. Combining the ratios, the simplest form of the ratio of juniors to adults is 6:1.
Step-by-step explanation:
The question involves finding the simplest form of the ratio of juniors to adults in a horse riding club, given two different ratios that relate children, juniors, and adults. First, we have the ratio of children juniors to adults as 3:1. Secondly, we know that the ratio of juniors to children is 2:5. The challenge is to find the ratio of juniors to adults in simplest form, assuming that 'children juniors' refers to the junior category.
To find this ratio, we need to set up a proportion that equates the number of juniors in both ratios. We'll represent the number of juniors as 'j', children as 'c', and adults as 'a'. From the given ratios, we have 3 parts juniors is to 1 part adult, which can be written as j/a = 3/1. We also have that 2 parts juniors is to 5 parts children, written as j/c = 2/5.
Since 'children' and 'children juniors' likely refer to the same group, we can use the ratio of juniors to children to adjust the number of juveniles in the first ratio. Multiplying the number of juveniles in the ratio of juniors to children (2) by the number of juveniles in the ratio of juniors to adults (3), we get 2 x 3 = 6. Doing the same for the number of adults (1) in the first ratio, since there is no change, we get 1 x 1 = 1.
Therefore, after combining the ratios, the new ratio of juniors to adults is 6:1.