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Finding the Third Proportional to 2,977 and 6,503

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Solution

The third proportional to 2,977 and 6,503 is: 14,205.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,977 : 6,503 = 6,503 : x
  2. Step 2: Convert to fraction form
    2,977/6,503 = 6,503/x
  3. Step 3: Cross multiply
    2,977x = 6,503 × 6,503
  4. Step 4: Simplify right side
    2,977x = 42,289,009
  5. Step 5: Solve for x
    x = 42,289,009/2,977
  6. Step 6: Final answer
    x = 14,205.24

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.