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Finding the Third Proportional to 19,534 and 27,830

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Solution

The third proportional to 19,534 and 27,830 is: 39,649.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,534 : 27,830 = 27,830 : x
  2. Step 2: Convert to fraction form
    19,534/27,830 = 27,830/x
  3. Step 3: Cross multiply
    19,534x = 27,830 × 27,830
  4. Step 4: Simplify right side
    19,534x = 774,508,900
  5. Step 5: Solve for x
    x = 774,508,900/19,534
  6. Step 6: Final answer
    x = 39,649.27

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.