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Finding the Third Proportional to 32,864 and 68,416

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Solution

The third proportional to 32,864 and 68,416 is: 142,427.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,864 : 68,416 = 68,416 : x
  2. Step 2: Convert to fraction form
    32,864/68,416 = 68,416/x
  3. Step 3: Cross multiply
    32,864x = 68,416 × 68,416
  4. Step 4: Simplify right side
    32,864x = 4,680,749,056
  5. Step 5: Solve for x
    x = 4,680,749,056/32,864
  6. Step 6: Final answer
    x = 142,427.86

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.