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Finding the Third Proportional to 9,684 and 22,742

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Solution

The third proportional to 9,684 and 22,742 is: 53,407.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,684 : 22,742 = 22,742 : x
  2. Step 2: Convert to fraction form
    9,684/22,742 = 22,742/x
  3. Step 3: Cross multiply
    9,684x = 22,742 × 22,742
  4. Step 4: Simplify right side
    9,684x = 517,198,564
  5. Step 5: Solve for x
    x = 517,198,564/9,684
  6. Step 6: Final answer
    x = 53,407.53

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.