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Finding the Third Proportional to 2,098 and 3,680

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Solution

The third proportional to 2,098 and 3,680 is: 6,454.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,098 : 3,680 = 3,680 : x
  2. Step 2: Convert to fraction form
    2,098/3,680 = 3,680/x
  3. Step 3: Cross multiply
    2,098x = 3,680 × 3,680
  4. Step 4: Simplify right side
    2,098x = 13,542,400
  5. Step 5: Solve for x
    x = 13,542,400/2,098
  6. Step 6: Final answer
    x = 6,454.91

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Why These Related Problems?

These problems maintain the same ratio (1.75) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.