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Finding the Third Proportional to 75,982 and 156,821

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Solution

The third proportional to 75,982 and 156,821 is: 323,666.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,982 : 156,821 = 156,821 : x
  2. Step 2: Convert to fraction form
    75,982/156,821 = 156,821/x
  3. Step 3: Cross multiply
    75,982x = 156,821 × 156,821
  4. Step 4: Simplify right side
    75,982x = 24,592,826,041
  5. Step 5: Solve for x
    x = 24,592,826,041/75,982
  6. Step 6: Final answer
    x = 323,666.47

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.