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Finding the Third Proportional to 523 and 861

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Solution

The third proportional to 523 and 861 is: 1,417.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 861 = 861 : x
  2. Step 2: Convert to fraction form
    523/861 = 861/x
  3. Step 3: Cross multiply
    523x = 861 × 861
  4. Step 4: Simplify right side
    523x = 741,321
  5. Step 5: Solve for x
    x = 741,321/523
  6. Step 6: Final answer
    x = 1,417.44

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Why These Related Problems?

These problems maintain the same ratio (1.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.