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Finding the Third Proportional to 264,541 and 397,415

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Solution

The third proportional to 264,541 and 397,415 is: 597,029.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    264,541 : 397,415 = 397,415 : x
  2. Step 2: Convert to fraction form
    264,541/397,415 = 397,415/x
  3. Step 3: Cross multiply
    264,541x = 397,415 × 397,415
  4. Step 4: Simplify right side
    264,541x = 157,938,682,225
  5. Step 5: Solve for x
    x = 157,938,682,225/264,541
  6. Step 6: Final answer
    x = 597,029.13

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.