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Finding the Third Proportional to 256,210 and 409,297

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Solution

The third proportional to 256,210 and 409,297 is: 653,854.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,210 : 409,297 = 409,297 : x
  2. Step 2: Convert to fraction form
    256,210/409,297 = 409,297/x
  3. Step 3: Cross multiply
    256,210x = 409,297 × 409,297
  4. Step 4: Simplify right side
    256,210x = 167,524,034,209
  5. Step 5: Solve for x
    x = 167,524,034,209/256,210
  6. Step 6: Final answer
    x = 653,854.39

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.