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Finding the Third Proportional to 814 and 1,784

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Solution

The third proportional to 814 and 1,784 is: 3,909.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    814 : 1,784 = 1,784 : x
  2. Step 2: Convert to fraction form
    814/1,784 = 1,784/x
  3. Step 3: Cross multiply
    814x = 1,784 × 1,784
  4. Step 4: Simplify right side
    814x = 3,182,656
  5. Step 5: Solve for x
    x = 3,182,656/814
  6. Step 6: Final answer
    x = 3,909.90

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.