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Finding the Third Proportional to 7,838 and 12,567

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Solution

The third proportional to 7,838 and 12,567 is: 20,149.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,838 : 12,567 = 12,567 : x
  2. Step 2: Convert to fraction form
    7,838/12,567 = 12,567/x
  3. Step 3: Cross multiply
    7,838x = 12,567 × 12,567
  4. Step 4: Simplify right side
    7,838x = 157,929,489
  5. Step 5: Solve for x
    x = 157,929,489/7,838
  6. Step 6: Final answer
    x = 20,149.21

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.