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Finding the Third Proportional to 82,507 and 127,973

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Solution

The third proportional to 82,507 and 127,973 is: 198,493.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,507 : 127,973 = 127,973 : x
  2. Step 2: Convert to fraction form
    82,507/127,973 = 127,973/x
  3. Step 3: Cross multiply
    82,507x = 127,973 × 127,973
  4. Step 4: Simplify right side
    82,507x = 16,377,088,729
  5. Step 5: Solve for x
    x = 16,377,088,729/82,507
  6. Step 6: Final answer
    x = 198,493.32

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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.