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Finding the Third Proportional to 38,524 and 84,096

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Solution

The third proportional to 38,524 and 84,096 is: 183,577.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,524 : 84,096 = 84,096 : x
  2. Step 2: Convert to fraction form
    38,524/84,096 = 84,096/x
  3. Step 3: Cross multiply
    38,524x = 84,096 × 84,096
  4. Step 4: Simplify right side
    38,524x = 7,072,137,216
  5. Step 5: Solve for x
    x = 7,072,137,216/38,524
  6. Step 6: Final answer
    x = 183,577.44

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.