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Finding the Third Proportional to 1,413 and 1,965

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Solution

The third proportional to 1,413 and 1,965 is: 2,732.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,413 : 1,965 = 1,965 : x
  2. Step 2: Convert to fraction form
    1,413/1,965 = 1,965/x
  3. Step 3: Cross multiply
    1,413x = 1,965 × 1,965
  4. Step 4: Simplify right side
    1,413x = 3,861,225
  5. Step 5: Solve for x
    x = 3,861,225/1,413
  6. Step 6: Final answer
    x = 2,732.64

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Why These Related Problems?

These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.