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Finding the Third Proportional to 3,840 and 8,424

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Solution

The third proportional to 3,840 and 8,424 is: 18,480.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,840 : 8,424 = 8,424 : x
  2. Step 2: Convert to fraction form
    3,840/8,424 = 8,424/x
  3. Step 3: Cross multiply
    3,840x = 8,424 × 8,424
  4. Step 4: Simplify right side
    3,840x = 70,963,776
  5. Step 5: Solve for x
    x = 70,963,776/3,840
  6. Step 6: Final answer
    x = 18,480.15

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.