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Finding the Third Proportional to 1,540 and 2,413

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Solution

The third proportional to 1,540 and 2,413 is: 3,780.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,540 : 2,413 = 2,413 : x
  2. Step 2: Convert to fraction form
    1,540/2,413 = 2,413/x
  3. Step 3: Cross multiply
    1,540x = 2,413 × 2,413
  4. Step 4: Simplify right side
    1,540x = 5,822,569
  5. Step 5: Solve for x
    x = 5,822,569/1,540
  6. Step 6: Final answer
    x = 3,780.89

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.