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Finding the Third Proportional to 82,058 and 193,197

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Solution

The third proportional to 82,058 and 193,197 is: 454,862.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,058 : 193,197 = 193,197 : x
  2. Step 2: Convert to fraction form
    82,058/193,197 = 193,197/x
  3. Step 3: Cross multiply
    82,058x = 193,197 × 193,197
  4. Step 4: Simplify right side
    82,058x = 37,325,080,809
  5. Step 5: Solve for x
    x = 37,325,080,809/82,058
  6. Step 6: Final answer
    x = 454,862.18

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.