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Finding the Third Proportional to 678 and 814

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Solution

The third proportional to 678 and 814 is: 977.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    678 : 814 = 814 : x
  2. Step 2: Convert to fraction form
    678/814 = 814/x
  3. Step 3: Cross multiply
    678x = 814 × 814
  4. Step 4: Simplify right side
    678x = 662,596
  5. Step 5: Solve for x
    x = 662,596/678
  6. Step 6: Final answer
    x = 977.28

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.