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Finding the Third Proportional to 97 and 223.06

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Solution

The third proportional to 97 and 223.06 is: 512.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    97 : 223.06 = 223.06 : x
  2. Step 2: Convert to fraction form
    97/223.06 = 223.06/x
  3. Step 3: Cross multiply
    97x = 223.06 × 223.06
  4. Step 4: Simplify right side
    97x = 49,756.88
  5. Step 5: Solve for x
    x = 49,756.88/97
  6. Step 6: Final answer
    x = 512.96

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.