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Finding the Third Proportional to 84,202 and 185,972

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Solution

The third proportional to 84,202 and 185,972 is: 410,745.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    84,202 : 185,972 = 185,972 : x
  2. Step 2: Convert to fraction form
    84,202/185,972 = 185,972/x
  3. Step 3: Cross multiply
    84,202x = 185,972 × 185,972
  4. Step 4: Simplify right side
    84,202x = 34,585,584,784
  5. Step 5: Solve for x
    x = 34,585,584,784/84,202
  6. Step 6: Final answer
    x = 410,745.41

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.