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Finding the Third Proportional to 165,742 and 257,097

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Solution

The third proportional to 165,742 and 257,097 is: 398,805.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    165,742 : 257,097 = 257,097 : x
  2. Step 2: Convert to fraction form
    165,742/257,097 = 257,097/x
  3. Step 3: Cross multiply
    165,742x = 257,097 × 257,097
  4. Step 4: Simplify right side
    165,742x = 66,098,867,409
  5. Step 5: Solve for x
    x = 66,098,867,409/165,742
  6. Step 6: Final answer
    x = 398,805.78

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.