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Finding the Third Proportional to 100,009 and 213,410

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Solution

The third proportional to 100,009 and 213,410 is: 455,397.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,009 : 213,410 = 213,410 : x
  2. Step 2: Convert to fraction form
    100,009/213,410 = 213,410/x
  3. Step 3: Cross multiply
    100,009x = 213,410 × 213,410
  4. Step 4: Simplify right side
    100,009x = 45,543,828,100
  5. Step 5: Solve for x
    x = 45,543,828,100/100,009
  6. Step 6: Final answer
    x = 455,397.30

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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.