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Finding the Third Proportional to 147,965 and 209,367

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Solution

The third proportional to 147,965 and 209,367 is: 296,249.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    147,965 : 209,367 = 209,367 : x
  2. Step 2: Convert to fraction form
    147,965/209,367 = 209,367/x
  3. Step 3: Cross multiply
    147,965x = 209,367 × 209,367
  4. Step 4: Simplify right side
    147,965x = 43,834,540,689
  5. Step 5: Solve for x
    x = 43,834,540,689/147,965
  6. Step 6: Final answer
    x = 296,249.39

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.