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Finding the Third Proportional to 83,541 and 197,142

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Solution

The third proportional to 83,541 and 197,142 is: 465,220.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,541 : 197,142 = 197,142 : x
  2. Step 2: Convert to fraction form
    83,541/197,142 = 197,142/x
  3. Step 3: Cross multiply
    83,541x = 197,142 × 197,142
  4. Step 4: Simplify right side
    83,541x = 38,864,968,164
  5. Step 5: Solve for x
    x = 38,864,968,164/83,541
  6. Step 6: Final answer
    x = 465,220.29

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.