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Finding the Third Proportional to 83,096 and 128,912

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Solution

The third proportional to 83,096 and 128,912 is: 199,989.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,096 : 128,912 = 128,912 : x
  2. Step 2: Convert to fraction form
    83,096/128,912 = 128,912/x
  3. Step 3: Cross multiply
    83,096x = 128,912 × 128,912
  4. Step 4: Simplify right side
    83,096x = 16,618,303,744
  5. Step 5: Solve for x
    x = 16,618,303,744/83,096
  6. Step 6: Final answer
    x = 199,989.21

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.