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Finding the Third Proportional to 120,180 and 278,206

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Solution

The third proportional to 120,180 and 278,206 is: 644,022.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    120,180 : 278,206 = 278,206 : x
  2. Step 2: Convert to fraction form
    120,180/278,206 = 278,206/x
  3. Step 3: Cross multiply
    120,180x = 278,206 × 278,206
  4. Step 4: Simplify right side
    120,180x = 77,398,578,436
  5. Step 5: Solve for x
    x = 77,398,578,436/120,180
  6. Step 6: Final answer
    x = 644,022.12

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.