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Finding the Third Proportional to 109.69 and 232.24

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Solution

The third proportional to 109.69 and 232.24 is: 491.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    109.69 : 232.24 = 232.24 : x
  2. Step 2: Convert to fraction form
    109.69/232.24 = 232.24/x
  3. Step 3: Cross multiply
    109.69x = 232.24 × 232.24
  4. Step 4: Simplify right side
    109.69x = 53,936.43
  5. Step 5: Solve for x
    x = 53,936.43/109.69
  6. Step 6: Final answer
    x = 491.73

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.