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Finding the Third Proportional to 4,646 and 6,977

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Solution

The third proportional to 4,646 and 6,977 is: 10,477.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,646 : 6,977 = 6,977 : x
  2. Step 2: Convert to fraction form
    4,646/6,977 = 6,977/x
  3. Step 3: Cross multiply
    4,646x = 6,977 × 6,977
  4. Step 4: Simplify right side
    4,646x = 48,678,529
  5. Step 5: Solve for x
    x = 48,678,529/4,646
  6. Step 6: Final answer
    x = 10,477.51

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.