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Finding the Third Proportional to 13,724 and 19,830

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Solution

The third proportional to 13,724 and 19,830 is: 28,652.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,724 : 19,830 = 19,830 : x
  2. Step 2: Convert to fraction form
    13,724/19,830 = 19,830/x
  3. Step 3: Cross multiply
    13,724x = 19,830 × 19,830
  4. Step 4: Simplify right side
    13,724x = 393,228,900
  5. Step 5: Solve for x
    x = 393,228,900/13,724
  6. Step 6: Final answer
    x = 28,652.65

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.