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Finding the Third Proportional to 2,709 and 2,941

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Solution

The third proportional to 2,709 and 2,941 is: 3,192.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,709 : 2,941 = 2,941 : x
  2. Step 2: Convert to fraction form
    2,709/2,941 = 2,941/x
  3. Step 3: Cross multiply
    2,709x = 2,941 × 2,941
  4. Step 4: Simplify right side
    2,709x = 8,649,481
  5. Step 5: Solve for x
    x = 8,649,481/2,709
  6. Step 6: Final answer
    x = 3,192.87

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.