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Finding the Third Proportional to 6,977 and 10,466

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Solution

The third proportional to 6,977 and 10,466 is: 15,699.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,977 : 10,466 = 10,466 : x
  2. Step 2: Convert to fraction form
    6,977/10,466 = 10,466/x
  3. Step 3: Cross multiply
    6,977x = 10,466 × 10,466
  4. Step 4: Simplify right side
    6,977x = 109,537,156
  5. Step 5: Solve for x
    x = 109,537,156/6,977
  6. Step 6: Final answer
    x = 15,699.75

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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.