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Finding the Third Proportional to 299,176 and 413,467

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Solution

The third proportional to 299,176 and 413,467 is: 571,419.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    299,176 : 413,467 = 413,467 : x
  2. Step 2: Convert to fraction form
    299,176/413,467 = 413,467/x
  3. Step 3: Cross multiply
    299,176x = 413,467 × 413,467
  4. Step 4: Simplify right side
    299,176x = 170,954,960,089
  5. Step 5: Solve for x
    x = 170,954,960,089/299,176
  6. Step 6: Final answer
    x = 571,419.37

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.