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Finding the Third Proportional to 296,414 and 459,667

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Solution

The third proportional to 296,414 and 459,667 is: 712,833.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    296,414 : 459,667 = 459,667 : x
  2. Step 2: Convert to fraction form
    296,414/459,667 = 459,667/x
  3. Step 3: Cross multiply
    296,414x = 459,667 × 459,667
  4. Step 4: Simplify right side
    296,414x = 211,293,750,889
  5. Step 5: Solve for x
    x = 211,293,750,889/296,414
  6. Step 6: Final answer
    x = 712,833.24

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.