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Finding the Third Proportional to 83,769 and 129,541

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Solution

The third proportional to 83,769 and 129,541 is: 200,323.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,769 : 129,541 = 129,541 : x
  2. Step 2: Convert to fraction form
    83,769/129,541 = 129,541/x
  3. Step 3: Cross multiply
    83,769x = 129,541 × 129,541
  4. Step 4: Simplify right side
    83,769x = 16,780,870,681
  5. Step 5: Solve for x
    x = 16,780,870,681/83,769
  6. Step 6: Final answer
    x = 200,323.16

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.