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Finding the Third Proportional to 51,786 and 77,652

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Solution

The third proportional to 51,786 and 77,652 is: 116,437.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,786 : 77,652 = 77,652 : x
  2. Step 2: Convert to fraction form
    51,786/77,652 = 77,652/x
  3. Step 3: Cross multiply
    51,786x = 77,652 × 77,652
  4. Step 4: Simplify right side
    51,786x = 6,029,833,104
  5. Step 5: Solve for x
    x = 6,029,833,104/51,786
  6. Step 6: Final answer
    x = 116,437.51

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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.