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Finding the Third Proportional to 100,410 and 214,164

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Solution

The third proportional to 100,410 and 214,164 is: 456,789.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,410 : 214,164 = 214,164 : x
  2. Step 2: Convert to fraction form
    100,410/214,164 = 214,164/x
  3. Step 3: Cross multiply
    100,410x = 214,164 × 214,164
  4. Step 4: Simplify right side
    100,410x = 45,866,218,896
  5. Step 5: Solve for x
    x = 45,866,218,896/100,410
  6. Step 6: Final answer
    x = 456,789.35

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.