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Finding the Third Proportional to 51,823 and 77,775

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Solution

The third proportional to 51,823 and 77,775 is: 116,723.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,823 : 77,775 = 77,775 : x
  2. Step 2: Convert to fraction form
    51,823/77,775 = 77,775/x
  3. Step 3: Cross multiply
    51,823x = 77,775 × 77,775
  4. Step 4: Simplify right side
    51,823x = 6,048,950,625
  5. Step 5: Solve for x
    x = 6,048,950,625/51,823
  6. Step 6: Final answer
    x = 116,723.28

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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.