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Finding the Third Proportional to 13,684 and 32,282

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Solution

The third proportional to 13,684 and 32,282 is: 76,156.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,684 : 32,282 = 32,282 : x
  2. Step 2: Convert to fraction form
    13,684/32,282 = 32,282/x
  3. Step 3: Cross multiply
    13,684x = 32,282 × 32,282
  4. Step 4: Simplify right side
    13,684x = 1,042,127,524
  5. Step 5: Solve for x
    x = 1,042,127,524/13,684
  6. Step 6: Final answer
    x = 76,156.64

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.