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Finding the Third Proportional to 270,461 and 420,434

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Solution

The third proportional to 270,461 and 420,434 is: 653,568.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    270,461 : 420,434 = 420,434 : x
  2. Step 2: Convert to fraction form
    270,461/420,434 = 420,434/x
  3. Step 3: Cross multiply
    270,461x = 420,434 × 420,434
  4. Step 4: Simplify right side
    270,461x = 176,764,748,356
  5. Step 5: Solve for x
    x = 176,764,748,356/270,461
  6. Step 6: Final answer
    x = 653,568.35

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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.