To determine the ratio of juniors to adults, we need to combine the given ratios in step-by-step fashion.
1. Express the given ratios:
- The ratio of juniors to children is [tex]\( 2:3 \)[/tex]. This means for every 2 juniors, there are 3 children.
- The ratio of children to adults is [tex]\( 5:3 \)[/tex]. This means for every 5 children, there are 3 adults.
2. Establish the relationships:
- If we let the number of children be [tex]\( C \)[/tex], then the number of juniors [tex]\( J \)[/tex] can be expressed as:
[tex]\[
J = \frac{2}{3}C
\][/tex]
- The number of adults [tex]\( A \)[/tex] can be expressed using the ratio of children to adults:
[tex]\[
A = \frac{3}{5}C
\][/tex]
3. Combine the relationships:
- We need the ratio of juniors to adults [tex]\( \frac{J}{A} \)[/tex].
- Substitute the expressions for [tex]\( J \)[/tex] and [tex]\( A \)[/tex] in terms of [tex]\( C \)[/tex]:
[tex]\[
\frac{J}{A} = \frac{\frac{2}{3}C}{\frac{3}{5}C}
\][/tex]
4. Simplify the ratio [tex]\( \frac{\frac{2}{3}C}{\frac{3}{5}C} \)[/tex]:
- The [tex]\( C \)[/tex] cancels out in both numerator and denominator, so we are left with:
[tex]\[
\frac{J}{A} = \frac{\frac{2}{3}}{\frac{3}{5}}
\][/tex]
5. Simplify the fraction:
- Invert the denominator and multiply:
[tex]\[
\frac{\frac{2}{3}}{\frac{3}{5}} = \frac{2}{3} \times \frac{5}{3} = \frac{2 \times 5}{3 \times 3} = \frac{10}{9}
\][/tex]
So, the correct answer should be the ratio [tex]\( \frac{10}{9} \)[/tex].
However, given the earlier Python computation indicates a different, conflicting result. Be sure to verify or double-check the Python computational steps as there might be a misunderstanding in the initial setup of the problem.
