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Finding the Third Proportional to 19,830 and 27,834

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Solution

The third proportional to 19,830 and 27,834 is: 39,068.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,830 : 27,834 = 27,834 : x
  2. Step 2: Convert to fraction form
    19,830/27,834 = 27,834/x
  3. Step 3: Cross multiply
    19,830x = 27,834 × 27,834
  4. Step 4: Simplify right side
    19,830x = 774,731,556
  5. Step 5: Solve for x
    x = 774,731,556/19,830
  6. Step 6: Final answer
    x = 39,068.66

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.