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Finding the Third Proportional to 37,584 and 81,729

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Solution

The third proportional to 37,584 and 81,729 is: 177,725.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,584 : 81,729 = 81,729 : x
  2. Step 2: Convert to fraction form
    37,584/81,729 = 81,729/x
  3. Step 3: Cross multiply
    37,584x = 81,729 × 81,729
  4. Step 4: Simplify right side
    37,584x = 6,679,629,441
  5. Step 5: Solve for x
    x = 6,679,629,441/37,584
  6. Step 6: Final answer
    x = 177,725.35

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.