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Finding the Third Proportional to 9,829 and 21,854

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Solution

The third proportional to 9,829 and 21,854 is: 48,590.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,829 : 21,854 = 21,854 : x
  2. Step 2: Convert to fraction form
    9,829/21,854 = 21,854/x
  3. Step 3: Cross multiply
    9,829x = 21,854 × 21,854
  4. Step 4: Simplify right side
    9,829x = 477,597,316
  5. Step 5: Solve for x
    x = 477,597,316/9,829
  6. Step 6: Final answer
    x = 48,590.63

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.