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Finding the Third Proportional to 51,780 and 81,842

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Solution

The third proportional to 51,780 and 81,842 is: 129,357.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,780 : 81,842 = 81,842 : x
  2. Step 2: Convert to fraction form
    51,780/81,842 = 81,842/x
  3. Step 3: Cross multiply
    51,780x = 81,842 × 81,842
  4. Step 4: Simplify right side
    51,780x = 6,698,112,964
  5. Step 5: Solve for x
    x = 6,698,112,964/51,780
  6. Step 6: Final answer
    x = 129,357.14

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.