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Finding the Third Proportional to 32,102 and 71,583

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Solution

The third proportional to 32,102 and 71,583 is: 159,620.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,102 : 71,583 = 71,583 : x
  2. Step 2: Convert to fraction form
    32,102/71,583 = 71,583/x
  3. Step 3: Cross multiply
    32,102x = 71,583 × 71,583
  4. Step 4: Simplify right side
    32,102x = 5,124,125,889
  5. Step 5: Solve for x
    x = 5,124,125,889/32,102
  6. Step 6: Final answer
    x = 159,620.14

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.