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Finding the Third Proportional to 9,728 and 14,416

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Solution

The third proportional to 9,728 and 14,416 is: 21,363.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,728 : 14,416 = 14,416 : x
  2. Step 2: Convert to fraction form
    9,728/14,416 = 14,416/x
  3. Step 3: Cross multiply
    9,728x = 14,416 × 14,416
  4. Step 4: Simplify right side
    9,728x = 207,821,056
  5. Step 5: Solve for x
    x = 207,821,056/9,728
  6. Step 6: Final answer
    x = 21,363.18

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.