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Finding the Third Proportional to 180,013 and 416,741

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Solution

The third proportional to 180,013 and 416,741 is: 964,780.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    180,013 : 416,741 = 416,741 : x
  2. Step 2: Convert to fraction form
    180,013/416,741 = 416,741/x
  3. Step 3: Cross multiply
    180,013x = 416,741 × 416,741
  4. Step 4: Simplify right side
    180,013x = 173,673,061,081
  5. Step 5: Solve for x
    x = 173,673,061,081/180,013
  6. Step 6: Final answer
    x = 964,780.66

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.