The ratio of Steven's age to Cindy's age is 3 : 2. The ratio of Cindy's age to Juliet's age is 4 : 5. What is the ratio of Steven's age to Juliet's age? Give your answer in the simplest form. Ans : ___

1. Identify the common term and find the equivalent ratios

Steven : Cindy = $3 : 2$
Cindy : Juliet = $4 : 5$
The common term is Cindy. We need to make Cindy's parts equal in both ratios. The lowest common multiple of $2$ and $4$ is $4$.
Multiply the first ratio by $2$:
Steven : Cindy = $(3 \times 2) : (2 \times 2) = 6 : 4$

2. Combine the ratios and extract the required ratio

Now we have:
Steven : Cindy : Juliet = $6 : 4 : 5$
The ratio of Steven's age to Juliet's age is $6 : 5$. This is already in its simplest form.