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Finding the Third Proportional to 100,096 and 214,176

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Solution

The third proportional to 100,096 and 214,176 is: 458,273.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,096 : 214,176 = 214,176 : x
  2. Step 2: Convert to fraction form
    100,096/214,176 = 214,176/x
  3. Step 3: Cross multiply
    100,096x = 214,176 × 214,176
  4. Step 4: Simplify right side
    100,096x = 45,871,358,976
  5. Step 5: Solve for x
    x = 45,871,358,976/100,096
  6. Step 6: Final answer
    x = 458,273.65

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.