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Finding the Third Proportional to 45,101 and 102,009

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Solution

The third proportional to 45,101 and 102,009 is: 230,722.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    45,101 : 102,009 = 102,009 : x
  2. Step 2: Convert to fraction form
    45,101/102,009 = 102,009/x
  3. Step 3: Cross multiply
    45,101x = 102,009 × 102,009
  4. Step 4: Simplify right side
    45,101x = 10,405,836,081
  5. Step 5: Solve for x
    x = 10,405,836,081/45,101
  6. Step 6: Final answer
    x = 230,722.96

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Why These Related Problems?

These problems maintain the same ratio (2.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.