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Finding the Third Proportional to 205,225 and 296,961

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Solution

The third proportional to 205,225 and 296,961 is: 429,703.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,225 : 296,961 = 296,961 : x
  2. Step 2: Convert to fraction form
    205,225/296,961 = 296,961/x
  3. Step 3: Cross multiply
    205,225x = 296,961 × 296,961
  4. Step 4: Simplify right side
    205,225x = 88,185,835,521
  5. Step 5: Solve for x
    x = 88,185,835,521/205,225
  6. Step 6: Final answer
    x = 429,703.18

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.