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Finding the Third Proportional to 10,414 and 23,587

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Solution

The third proportional to 10,414 and 23,587 is: 53,422.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,414 : 23,587 = 23,587 : x
  2. Step 2: Convert to fraction form
    10,414/23,587 = 23,587/x
  3. Step 3: Cross multiply
    10,414x = 23,587 × 23,587
  4. Step 4: Simplify right side
    10,414x = 556,346,569
  5. Step 5: Solve for x
    x = 556,346,569/10,414
  6. Step 6: Final answer
    x = 53,422.95

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Why These Related Problems?

These problems maintain the same ratio (2.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.