The problem asks:

"The ratio of the number of boys in a school play to the total number of students in the play is $\frac{7}{10}$. What is the ratio of the number of girls in the play to the number of boys in the play?"

Step-by-step solution:

1. Understanding the given ratio:

   • The ratio of boys to the total number of students is $\frac{7}{10}$.
   • This means that for every 10 students, 7 are boys.

2. Finding the ratio of girls to boys:

   • Since the total number of students is 10, the number of girls can be found by subtracting the number of boys from the total: $\text{Number of girls} = 10 - 7 = 3.$
   • Therefore, the number of girls is 3 and the number of boys is 7.

3. Ratio of girls to boys:

   • The ratio of girls to boys is: $\frac{\text{Number of girls}}{\text{Number of boys}} = \frac{3}{7}.$

Thus, the ratio of the number of girls to the number of boys is $\frac{3}{7}$.

Do you want further details on any part of the solution? Here are 5 related questions to expand your understanding:

1. How can we interpret ratios in real-life situations like this?
2. If the ratio of girls to total students was given, how would the approach change?
3. How do you convert a ratio into a percentage?
4. Can you solve a similar problem if the ratio of girls to total students was 4:10?
5. What would the ratio be if the total number of students increased?

Tip: Always subtract the given quantity from the total when solving ratio problems involving part-to-whole relationships.