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Finding the Third Proportional to 1,682 and 2,977

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Solution

The third proportional to 1,682 and 2,977 is: 5,269.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,682 : 2,977 = 2,977 : x
  2. Step 2: Convert to fraction form
    1,682/2,977 = 2,977/x
  3. Step 3: Cross multiply
    1,682x = 2,977 × 2,977
  4. Step 4: Simplify right side
    1,682x = 8,862,529
  5. Step 5: Solve for x
    x = 8,862,529/1,682
  6. Step 6: Final answer
    x = 5,269.04

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.