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Finding the Third Proportional to 780 and 1,542

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Solution

The third proportional to 780 and 1,542 is: 3,048.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    780 : 1,542 = 1,542 : x
  2. Step 2: Convert to fraction form
    780/1,542 = 1,542/x
  3. Step 3: Cross multiply
    780x = 1,542 × 1,542
  4. Step 4: Simplify right side
    780x = 2,377,764
  5. Step 5: Solve for x
    x = 2,377,764/780
  6. Step 6: Final answer
    x = 3,048.42

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Why These Related Problems?

These problems maintain the same ratio (1.98) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.