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Finding the Third Proportional to 51,438 and 77,166

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Solution

The third proportional to 51,438 and 77,166 is: 115,762.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,438 : 77,166 = 77,166 : x
  2. Step 2: Convert to fraction form
    51,438/77,166 = 77,166/x
  3. Step 3: Cross multiply
    51,438x = 77,166 × 77,166
  4. Step 4: Simplify right side
    51,438x = 5,954,591,556
  5. Step 5: Solve for x
    x = 5,954,591,556/51,438
  6. Step 6: Final answer
    x = 115,762.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.