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Finding the Third Proportional to 77,684 and 113,972

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Solution

The third proportional to 77,684 and 113,972 is: 167,210.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,684 : 113,972 = 113,972 : x
  2. Step 2: Convert to fraction form
    77,684/113,972 = 113,972/x
  3. Step 3: Cross multiply
    77,684x = 113,972 × 113,972
  4. Step 4: Simplify right side
    77,684x = 12,989,616,784
  5. Step 5: Solve for x
    x = 12,989,616,784/77,684
  6. Step 6: Final answer
    x = 167,210.97

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.