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Finding the Third Proportional to 65,898 and 102,114

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Solution

The third proportional to 65,898 and 102,114 is: 158,233.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,898 : 102,114 = 102,114 : x
  2. Step 2: Convert to fraction form
    65,898/102,114 = 102,114/x
  3. Step 3: Cross multiply
    65,898x = 102,114 × 102,114
  4. Step 4: Simplify right side
    65,898x = 10,427,268,996
  5. Step 5: Solve for x
    x = 10,427,268,996/65,898
  6. Step 6: Final answer
    x = 158,233.47

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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.