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Finding the Third Proportional to 84,415 and 197,213

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Solution

The third proportional to 84,415 and 197,213 is: 460,735.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    84,415 : 197,213 = 197,213 : x
  2. Step 2: Convert to fraction form
    84,415/197,213 = 197,213/x
  3. Step 3: Cross multiply
    84,415x = 197,213 × 197,213
  4. Step 4: Simplify right side
    84,415x = 38,892,967,369
  5. Step 5: Solve for x
    x = 38,892,967,369/84,415
  6. Step 6: Final answer
    x = 460,735.26

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.