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Finding the Third Proportional to 214.78 and 478.78

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Solution

The third proportional to 214.78 and 478.78 is: 1,067.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.78 : 478.78 = 478.78 : x
  2. Step 2: Convert to fraction form
    214.78/478.78 = 478.78/x
  3. Step 3: Cross multiply
    214.78x = 478.78 × 478.78
  4. Step 4: Simplify right side
    214.78x = 229,231.49
  5. Step 5: Solve for x
    x = 229,231.49/214.78
  6. Step 6: Final answer
    x = 1,067.28

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.