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Finding the Third Proportional to 205.13 and 299.63

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Solution

The third proportional to 205.13 and 299.63 is: 437.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.13 : 299.63 = 299.63 : x
  2. Step 2: Convert to fraction form
    205.13/299.63 = 299.63/x
  3. Step 3: Cross multiply
    205.13x = 299.63 × 299.63
  4. Step 4: Simplify right side
    205.13x = 89,775.14
  5. Step 5: Solve for x
    x = 89,775.14/205.13
  6. Step 6: Final answer
    x = 437.66

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.