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Finding the Third Proportional to 180,414 and 256,443

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Solution

The third proportional to 180,414 and 256,443 is: 364,511.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    180,414 : 256,443 = 256,443 : x
  2. Step 2: Convert to fraction form
    180,414/256,443 = 256,443/x
  3. Step 3: Cross multiply
    180,414x = 256,443 × 256,443
  4. Step 4: Simplify right side
    180,414x = 65,763,012,249
  5. Step 5: Solve for x
    x = 65,763,012,249/180,414
  6. Step 6: Final answer
    x = 364,511.69

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.