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Finding the Third Proportional to 51,305 and 77,106

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Solution

The third proportional to 51,305 and 77,106 is: 115,882.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,305 : 77,106 = 77,106 : x
  2. Step 2: Convert to fraction form
    51,305/77,106 = 77,106/x
  3. Step 3: Cross multiply
    51,305x = 77,106 × 77,106
  4. Step 4: Simplify right side
    51,305x = 5,945,335,236
  5. Step 5: Solve for x
    x = 5,945,335,236/51,305
  6. Step 6: Final answer
    x = 115,882.18

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.