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Finding the Third Proportional to 10,414 and 15,970

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Solution

The third proportional to 10,414 and 15,970 is: 24,490.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,414 : 15,970 = 15,970 : x
  2. Step 2: Convert to fraction form
    10,414/15,970 = 15,970/x
  3. Step 3: Cross multiply
    10,414x = 15,970 × 15,970
  4. Step 4: Simplify right side
    10,414x = 255,040,900
  5. Step 5: Solve for x
    x = 255,040,900/10,414
  6. Step 6: Final answer
    x = 24,490.20

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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.