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Finding the Third Proportional to 205,228 and 296,964

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Solution

The third proportional to 205,228 and 296,964 is: 429,705.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,228 : 296,964 = 296,964 : x
  2. Step 2: Convert to fraction form
    205,228/296,964 = 296,964/x
  3. Step 3: Cross multiply
    205,228x = 296,964 × 296,964
  4. Step 4: Simplify right side
    205,228x = 88,187,617,296
  5. Step 5: Solve for x
    x = 88,187,617,296/205,228
  6. Step 6: Final answer
    x = 429,705.58

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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.