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Finding the Third Proportional to 256,889 and 409,116

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Solution

The third proportional to 256,889 and 409,116 is: 651,549.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,889 : 409,116 = 409,116 : x
  2. Step 2: Convert to fraction form
    256,889/409,116 = 409,116/x
  3. Step 3: Cross multiply
    256,889x = 409,116 × 409,116
  4. Step 4: Simplify right side
    256,889x = 167,375,901,456
  5. Step 5: Solve for x
    x = 167,375,901,456/256,889
  6. Step 6: Final answer
    x = 651,549.51

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.