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Finding the Third Proportional to 1,413 and 1,902

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Solution

The third proportional to 1,413 and 1,902 is: 2,560.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,413 : 1,902 = 1,902 : x
  2. Step 2: Convert to fraction form
    1,413/1,902 = 1,902/x
  3. Step 3: Cross multiply
    1,413x = 1,902 × 1,902
  4. Step 4: Simplify right side
    1,413x = 3,617,604
  5. Step 5: Solve for x
    x = 3,617,604/1,413
  6. Step 6: Final answer
    x = 2,560.23

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These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.