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Finding the Third Proportional to 77,982 and 164,112

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Solution

The third proportional to 77,982 and 164,112 is: 345,371.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,982 : 164,112 = 164,112 : x
  2. Step 2: Convert to fraction form
    77,982/164,112 = 164,112/x
  3. Step 3: Cross multiply
    77,982x = 164,112 × 164,112
  4. Step 4: Simplify right side
    77,982x = 26,932,748,544
  5. Step 5: Solve for x
    x = 26,932,748,544/77,982
  6. Step 6: Final answer
    x = 345,371.35

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.