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Finding the Third Proportional to 378.38 and 431.06

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Solution

The third proportional to 378.38 and 431.06 is: 491.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    378.38 : 431.06 = 431.06 : x
  2. Step 2: Convert to fraction form
    378.38/431.06 = 431.06/x
  3. Step 3: Cross multiply
    378.38x = 431.06 × 431.06
  4. Step 4: Simplify right side
    378.38x = 185,814.88
  5. Step 5: Solve for x
    x = 185,814.88/378.38
  6. Step 6: Final answer
    x = 491.09

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.