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Finding the Third Proportional to 10,420 and 14,238

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Solution

The third proportional to 10,420 and 14,238 is: 19,454.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,420 : 14,238 = 14,238 : x
  2. Step 2: Convert to fraction form
    10,420/14,238 = 14,238/x
  3. Step 3: Cross multiply
    10,420x = 14,238 × 14,238
  4. Step 4: Simplify right side
    10,420x = 202,720,644
  5. Step 5: Solve for x
    x = 202,720,644/10,420
  6. Step 6: Final answer
    x = 19,454.96

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.