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Finding the Third Proportional to 84,216 and 180,102

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Solution

The third proportional to 84,216 and 180,102 is: 385,161.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    84,216 : 180,102 = 180,102 : x
  2. Step 2: Convert to fraction form
    84,216/180,102 = 180,102/x
  3. Step 3: Cross multiply
    84,216x = 180,102 × 180,102
  4. Step 4: Simplify right side
    84,216x = 32,436,730,404
  5. Step 5: Solve for x
    x = 32,436,730,404/84,216
  6. Step 6: Final answer
    x = 385,161.14

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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.