The given ratio equation is written as:

\[
\frac{7}{3} : z :: 21 : 50
\]

This means that the ratios are proportional:

\[
\frac{7}{3} = \frac{21}{50}
\]

Now, to solve for \( z \), we cross-multiply:

\[
7 \times 50 = 3 \times 21
\]

Simplifying both sides:

\[
350 = 3z
\]

Now, divide both sides by 3 to isolate \( z \):

\[
z = \frac{350}{3} = 116.67
\]

Thus, the value of \( z \) is approximately \( 116.67 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What are the properties of proportional relationships?
2. How can you check if two ratios are proportional?
3. Can cross-multiplication be used for any ratio?
4. How do you solve a proportion with three unknowns?
5. What is the importance of ratios in real-life applications?

**Tip:** Always simplify ratios when possible to make solving proportions easier.

Learn how to solve the proportion z:7/3::21:50 using cross-multiplication. This detailed step-by-step guide covers key mathematical concepts of ratios and proportions, ideal for students in Grades 6-8.

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