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Finding the Third Proportional to 102,400 and 212,976

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Solution

The third proportional to 102,400 and 212,976 is: 442,956.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,400 : 212,976 = 212,976 : x
  2. Step 2: Convert to fraction form
    102,400/212,976 = 212,976/x
  3. Step 3: Cross multiply
    102,400x = 212,976 × 212,976
  4. Step 4: Simplify right side
    102,400x = 45,358,776,576
  5. Step 5: Solve for x
    x = 45,358,776,576/102,400
  6. Step 6: Final answer
    x = 442,956.80

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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.