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Finding the Third Proportional to 291,434 and 463,407

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Solution

The third proportional to 291,434 and 463,407 is: 736,859.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    291,434 : 463,407 = 463,407 : x
  2. Step 2: Convert to fraction form
    291,434/463,407 = 463,407/x
  3. Step 3: Cross multiply
    291,434x = 463,407 × 463,407
  4. Step 4: Simplify right side
    291,434x = 214,746,047,649
  5. Step 5: Solve for x
    x = 214,746,047,649/291,434
  6. Step 6: Final answer
    x = 736,859.97

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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.