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Finding the Third Proportional to 51,689 and 77,534

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Solution

The third proportional to 51,689 and 77,534 is: 116,301.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,689 : 77,534 = 77,534 : x
  2. Step 2: Convert to fraction form
    51,689/77,534 = 77,534/x
  3. Step 3: Cross multiply
    51,689x = 77,534 × 77,534
  4. Step 4: Simplify right side
    51,689x = 6,011,521,156
  5. Step 5: Solve for x
    x = 6,011,521,156/51,689
  6. Step 6: Final answer
    x = 116,301.75

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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.