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Finding the Third Proportional to 4,564 and 9,856

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Solution

The third proportional to 4,564 and 9,856 is: 21,284.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,564 : 9,856 = 9,856 : x
  2. Step 2: Convert to fraction form
    4,564/9,856 = 9,856/x
  3. Step 3: Cross multiply
    4,564x = 9,856 × 9,856
  4. Step 4: Simplify right side
    4,564x = 97,140,736
  5. Step 5: Solve for x
    x = 97,140,736/4,564
  6. Step 6: Final answer
    x = 21,284.12

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.