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Finding the Third Proportional to 75,690 and 102,842

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Solution

The third proportional to 75,690 and 102,842 is: 139,734.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,690 : 102,842 = 102,842 : x
  2. Step 2: Convert to fraction form
    75,690/102,842 = 102,842/x
  3. Step 3: Cross multiply
    75,690x = 102,842 × 102,842
  4. Step 4: Simplify right side
    75,690x = 10,576,476,964
  5. Step 5: Solve for x
    x = 10,576,476,964/75,690
  6. Step 6: Final answer
    x = 139,734.14

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.