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Finding the Third Proportional to 65,906 and 102,011

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Solution

The third proportional to 65,906 and 102,011 is: 157,895.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,906 : 102,011 = 102,011 : x
  2. Step 2: Convert to fraction form
    65,906/102,011 = 102,011/x
  3. Step 3: Cross multiply
    65,906x = 102,011 × 102,011
  4. Step 4: Simplify right side
    65,906x = 10,406,244,121
  5. Step 5: Solve for x
    x = 10,406,244,121/65,906
  6. Step 6: Final answer
    x = 157,895.25

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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.