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Finding the Third Proportional to 210,414 and 295,965

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Solution

The third proportional to 210,414 and 295,965 is: 416,299.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    210,414 : 295,965 = 295,965 : x
  2. Step 2: Convert to fraction form
    210,414/295,965 = 295,965/x
  3. Step 3: Cross multiply
    210,414x = 295,965 × 295,965
  4. Step 4: Simplify right side
    210,414x = 87,595,281,225
  5. Step 5: Solve for x
    x = 87,595,281,225/210,414
  6. Step 6: Final answer
    x = 416,299.68

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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.