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Finding the Third Proportional to 2,003 and 2,414

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Solution

The third proportional to 2,003 and 2,414 is: 2,909.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,003 : 2,414 = 2,414 : x
  2. Step 2: Convert to fraction form
    2,003/2,414 = 2,414/x
  3. Step 3: Cross multiply
    2,003x = 2,414 × 2,414
  4. Step 4: Simplify right side
    2,003x = 5,827,396
  5. Step 5: Solve for x
    x = 5,827,396/2,003
  6. Step 6: Final answer
    x = 2,909.33

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.