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Finding the Third Proportional to 309 and 462.13

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Solution

The third proportional to 309 and 462.13 is: 691.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    309 : 462.13 = 462.13 : x
  2. Step 2: Convert to fraction form
    309/462.13 = 462.13/x
  3. Step 3: Cross multiply
    309x = 462.13 × 462.13
  4. Step 4: Simplify right side
    309x = 213,559.52
  5. Step 5: Solve for x
    x = 213,559.52/309
  6. Step 6: Final answer
    x = 691.13

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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.