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Finding the Third Proportional to 199.78 and 420.09

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Solution

The third proportional to 199.78 and 420.09 is: 883.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    199.78 : 420.09 = 420.09 : x
  2. Step 2: Convert to fraction form
    199.78/420.09 = 420.09/x
  3. Step 3: Cross multiply
    199.78x = 420.09 × 420.09
  4. Step 4: Simplify right side
    199.78x = 176,478.76
  5. Step 5: Solve for x
    x = 176,478.76/199.78
  6. Step 6: Final answer
    x = 883.36

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.