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Finding the Third Proportional to 411,223 and 645,235

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Solution

The third proportional to 411,223 and 645,235 is: 1,012,414.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    411,223 : 645,235 = 645,235 : x
  2. Step 2: Convert to fraction form
    411,223/645,235 = 645,235/x
  3. Step 3: Cross multiply
    411,223x = 645,235 × 645,235
  4. Step 4: Simplify right side
    411,223x = 416,328,205,225
  5. Step 5: Solve for x
    x = 416,328,205,225/411,223
  6. Step 6: Final answer
    x = 1,012,414.69

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.