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Finding the Third Proportional to 199.97 and 410.06

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Solution

The third proportional to 199.97 and 410.06 is: 840.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    199.97 : 410.06 = 410.06 : x
  2. Step 2: Convert to fraction form
    199.97/410.06 = 410.06/x
  3. Step 3: Cross multiply
    199.97x = 410.06 × 410.06
  4. Step 4: Simplify right side
    199.97x = 168,151.25
  5. Step 5: Solve for x
    x = 168,151.25/199.97
  6. Step 6: Final answer
    x = 840.89

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.