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Finding the Third Proportional to 1,420 and 3,413

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Solution

The third proportional to 1,420 and 3,413 is: 8,203.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,420 : 3,413 = 3,413 : x
  2. Step 2: Convert to fraction form
    1,420/3,413 = 3,413/x
  3. Step 3: Cross multiply
    1,420x = 3,413 × 3,413
  4. Step 4: Simplify right side
    1,420x = 11,648,569
  5. Step 5: Solve for x
    x = 11,648,569/1,420
  6. Step 6: Final answer
    x = 8,203.22

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Why These Related Problems?

These problems maintain the same ratio (2.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.