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Finding the Third Proportional to 224,414 and 491,057

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Solution

The third proportional to 224,414 and 491,057 is: 1,074,518.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    224,414 : 491,057 = 491,057 : x
  2. Step 2: Convert to fraction form
    224,414/491,057 = 491,057/x
  3. Step 3: Cross multiply
    224,414x = 491,057 × 491,057
  4. Step 4: Simplify right side
    224,414x = 241,136,977,249
  5. Step 5: Solve for x
    x = 241,136,977,249/224,414
  6. Step 6: Final answer
    x = 1,074,518.42

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.