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Finding the Third Proportional to 84,214 and 180,097

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Solution

The third proportional to 84,214 and 180,097 is: 385,148.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    84,214 : 180,097 = 180,097 : x
  2. Step 2: Convert to fraction form
    84,214/180,097 = 180,097/x
  3. Step 3: Cross multiply
    84,214x = 180,097 × 180,097
  4. Step 4: Simplify right side
    84,214x = 32,434,929,409
  5. Step 5: Solve for x
    x = 32,434,929,409/84,214
  6. Step 6: Final answer
    x = 385,148.90

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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.