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Finding the Third Proportional to 144,519 and 205,421

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Solution

The third proportional to 144,519 and 205,421 is: 291,987.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    144,519 : 205,421 = 205,421 : x
  2. Step 2: Convert to fraction form
    144,519/205,421 = 205,421/x
  3. Step 3: Cross multiply
    144,519x = 205,421 × 205,421
  4. Step 4: Simplify right side
    144,519x = 42,197,787,241
  5. Step 5: Solve for x
    x = 42,197,787,241/144,519
  6. Step 6: Final answer
    x = 291,987.82

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.