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Finding the Third Proportional to 51,705 and 106,731

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Solution

The third proportional to 51,705 and 106,731 is: 220,317.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,705 : 106,731 = 106,731 : x
  2. Step 2: Convert to fraction form
    51,705/106,731 = 106,731/x
  3. Step 3: Cross multiply
    51,705x = 106,731 × 106,731
  4. Step 4: Simplify right side
    51,705x = 11,391,506,361
  5. Step 5: Solve for x
    x = 11,391,506,361/51,705
  6. Step 6: Final answer
    x = 220,317.31

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.