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Finding the Third Proportional to 177,984 and 413,856

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Solution

The third proportional to 177,984 and 413,856 is: 962,315.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    177,984 : 413,856 = 413,856 : x
  2. Step 2: Convert to fraction form
    177,984/413,856 = 413,856/x
  3. Step 3: Cross multiply
    177,984x = 413,856 × 413,856
  4. Step 4: Simplify right side
    177,984x = 171,276,788,736
  5. Step 5: Solve for x
    x = 171,276,788,736/177,984
  6. Step 6: Final answer
    x = 962,315.65

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.