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Finding the Third Proportional to 291,433 and 463,406

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Solution

The third proportional to 291,433 and 463,406 is: 736,859.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    291,433 : 463,406 = 463,406 : x
  2. Step 2: Convert to fraction form
    291,433/463,406 = 463,406/x
  3. Step 3: Cross multiply
    291,433x = 463,406 × 463,406
  4. Step 4: Simplify right side
    291,433x = 214,745,120,836
  5. Step 5: Solve for x
    x = 214,745,120,836/291,433
  6. Step 6: Final answer
    x = 736,859.32

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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.