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Finding the Third Proportional to 211.78 and 491.91

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Solution

The third proportional to 211.78 and 491.91 is: 1,142.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    211.78 : 491.91 = 491.91 : x
  2. Step 2: Convert to fraction form
    211.78/491.91 = 491.91/x
  3. Step 3: Cross multiply
    211.78x = 491.91 × 491.91
  4. Step 4: Simplify right side
    211.78x = 241,971.76
  5. Step 5: Solve for x
    x = 241,971.76/211.78
  6. Step 6: Final answer
    x = 1,142.56

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.