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Finding the Third Proportional to 205.41 and 456.38

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Solution

The third proportional to 205.41 and 456.38 is: 1,013.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.41 : 456.38 = 456.38 : x
  2. Step 2: Convert to fraction form
    205.41/456.38 = 456.38/x
  3. Step 3: Cross multiply
    205.41x = 456.38 × 456.38
  4. Step 4: Simplify right side
    205.41x = 208,278.14
  5. Step 5: Solve for x
    x = 208,278.14/205.41
  6. Step 6: Final answer
    x = 1,013.98

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.