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Finding the Third Proportional to 186,458 and 415,012

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Solution

The third proportional to 186,458 and 415,012 is: 923,719.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    186,458 : 415,012 = 415,012 : x
  2. Step 2: Convert to fraction form
    186,458/415,012 = 415,012/x
  3. Step 3: Cross multiply
    186,458x = 415,012 × 415,012
  4. Step 4: Simplify right side
    186,458x = 172,234,960,144
  5. Step 5: Solve for x
    x = 172,234,960,144/186,458
  6. Step 6: Final answer
    x = 923,719.87

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.