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Finding the Third Proportional to 51,790 and 77,830

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Solution

The third proportional to 51,790 and 77,830 is: 116,962.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,790 : 77,830 = 77,830 : x
  2. Step 2: Convert to fraction form
    51,790/77,830 = 77,830/x
  3. Step 3: Cross multiply
    51,790x = 77,830 × 77,830
  4. Step 4: Simplify right side
    51,790x = 6,057,508,900
  5. Step 5: Solve for x
    x = 6,057,508,900/51,790
  6. Step 6: Final answer
    x = 116,962.91

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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.