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Finding the Third Proportional to 291,441 and 463,419

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Solution

The third proportional to 291,441 and 463,419 is: 736,880.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    291,441 : 463,419 = 463,419 : x
  2. Step 2: Convert to fraction form
    291,441/463,419 = 463,419/x
  3. Step 3: Cross multiply
    291,441x = 463,419 × 463,419
  4. Step 4: Simplify right side
    291,441x = 214,757,169,561
  5. Step 5: Solve for x
    x = 214,757,169,561/291,441
  6. Step 6: Final answer
    x = 736,880.43

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.