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Finding the Third Proportional to 309 and 462.38

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Solution

The third proportional to 309 and 462.38 is: 691.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    309 : 462.38 = 462.38 : x
  2. Step 2: Convert to fraction form
    309/462.38 = 462.38/x
  3. Step 3: Cross multiply
    309x = 462.38 × 462.38
  4. Step 4: Simplify right side
    309x = 213,790.64
  5. Step 5: Solve for x
    x = 213,790.64/309
  6. Step 6: Final answer
    x = 691.88

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.