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Finding the Third Proportional to 977 and 1,766

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Solution

The third proportional to 977 and 1,766 is: 3,192.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    977 : 1,766 = 1,766 : x
  2. Step 2: Convert to fraction form
    977/1,766 = 1,766/x
  3. Step 3: Cross multiply
    977x = 1,766 × 1,766
  4. Step 4: Simplify right side
    977x = 3,118,756
  5. Step 5: Solve for x
    x = 3,118,756/977
  6. Step 6: Final answer
    x = 3,192.18

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Why These Related Problems?

These problems maintain the same ratio (1.81) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.