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Finding the Third Proportional to 828 and 1,413

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Solution

The third proportional to 828 and 1,413 is: 2,411.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    828 : 1,413 = 1,413 : x
  2. Step 2: Convert to fraction form
    828/1,413 = 1,413/x
  3. Step 3: Cross multiply
    828x = 1,413 × 1,413
  4. Step 4: Simplify right side
    828x = 1,996,569
  5. Step 5: Solve for x
    x = 1,996,569/828
  6. Step 6: Final answer
    x = 2,411.32

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Why These Related Problems?

These problems maintain the same ratio (1.71) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.