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Finding the Third Proportional to 680 and 1,600

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Solution

The third proportional to 680 and 1,600 is: 3,764.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    680 : 1,600 = 1,600 : x
  2. Step 2: Convert to fraction form
    680/1,600 = 1,600/x
  3. Step 3: Cross multiply
    680x = 1,600 × 1,600
  4. Step 4: Simplify right side
    680x = 2,560,000
  5. Step 5: Solve for x
    x = 2,560,000/680
  6. Step 6: Final answer
    x = 3,764.71

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.