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Finding the Third Proportional to 280,964 and 419,784

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Solution

The third proportional to 280,964 and 419,784 is: 627,192.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    280,964 : 419,784 = 419,784 : x
  2. Step 2: Convert to fraction form
    280,964/419,784 = 419,784/x
  3. Step 3: Cross multiply
    280,964x = 419,784 × 419,784
  4. Step 4: Simplify right side
    280,964x = 176,218,606,656
  5. Step 5: Solve for x
    x = 176,218,606,656/280,964
  6. Step 6: Final answer
    x = 627,192.83

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.