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Finding the Third Proportional to 209.75 and 463.38

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Solution

The third proportional to 209.75 and 463.38 is: 1,023.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.75 : 463.38 = 463.38 : x
  2. Step 2: Convert to fraction form
    209.75/463.38 = 463.38/x
  3. Step 3: Cross multiply
    209.75x = 463.38 × 463.38
  4. Step 4: Simplify right side
    209.75x = 214,716.39
  5. Step 5: Solve for x
    x = 214,716.39/209.75
  6. Step 6: Final answer
    x = 1,023.68

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.