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Finding the Third Proportional to 1,780 and 4,042

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Solution

The third proportional to 1,780 and 4,042 is: 9,178.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,780 : 4,042 = 4,042 : x
  2. Step 2: Convert to fraction form
    1,780/4,042 = 4,042/x
  3. Step 3: Cross multiply
    1,780x = 4,042 × 4,042
  4. Step 4: Simplify right side
    1,780x = 16,337,764
  5. Step 5: Solve for x
    x = 16,337,764/1,780
  6. Step 6: Final answer
    x = 9,178.52

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Why These Related Problems?

These problems maintain the same ratio (2.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.