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Finding the Third Proportional to 6,783 and 10,407

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Solution

The third proportional to 6,783 and 10,407 is: 15,967.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,783 : 10,407 = 10,407 : x
  2. Step 2: Convert to fraction form
    6,783/10,407 = 10,407/x
  3. Step 3: Cross multiply
    6,783x = 10,407 × 10,407
  4. Step 4: Simplify right side
    6,783x = 108,305,649
  5. Step 5: Solve for x
    x = 108,305,649/6,783
  6. Step 6: Final answer
    x = 15,967.22

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.