The value of $x$ where $x : 2\frac{1}{3} : : 21 : 50$ is

### Concept & Proportion In a proportion where four terms are related as $a : b : : c : d$, the product of the extreme terms (outer terms) is equal to the product of the mean terms (inner terms). $$ a \times d = b \times c $$ ### Step-by-Step Solution * **Given:** The proportion is $x : 2\frac{1}{3} : : 21 : 50$. * **Convert mixed fraction:** Convert $2\frac{1}{3}$ to an improper fraction: $\frac{(2 \times 3) + 1}{3} = \frac{7}{3}$. * **Set up the equation:** Use the product of extremes equals product of means rule. $x \times 50 = \frac{7}{3} \times 21$ * **Simplify:** $50x = 7 \times 7$ $50x = 49$ * **Solve for $x$:** $x = \frac{49}{50}$ ### Exam Strategy & Shortcut Treat the proportion as equivalent fractions: $\frac{x}{7/3} = \frac{21}{50}$. Simply cross-multiply the $7/3$ to the right side: $x = \frac{21 \times (7/3)}{50}$. The $3$ cancels into the $21$ giving $7$. So, $x = \frac{7 \times 7}{50} = \frac{49}{50}$. ### Common Pitfall A frequent mistake is improperly converting the mixed number $2\frac{1}{3}$, or incorrectly pairing the extremes and means, leading to a flipped fraction. ### Final Answer Therefore, the correct answer is **$\frac{49}{50}$**.