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Finding the Third Proportional to 206.40 and 422.30

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Solution

The third proportional to 206.40 and 422.30 is: 864.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    206.40 : 422.30 = 422.30 : x
  2. Step 2: Convert to fraction form
    206.40/422.30 = 422.30/x
  3. Step 3: Cross multiply
    206.40x = 422.30 × 422.30
  4. Step 4: Simplify right side
    206.40x = 178,334.65
  5. Step 5: Solve for x
    x = 178,334.65/206.40
  6. Step 6: Final answer
    x = 864.01

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.