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Finding the Third Proportional to 166.85 and 257.84

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Solution

The third proportional to 166.85 and 257.84 is: 398.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    166.85 : 257.84 = 257.84 : x
  2. Step 2: Convert to fraction form
    166.85/257.84 = 257.84/x
  3. Step 3: Cross multiply
    166.85x = 257.84 × 257.84
  4. Step 4: Simplify right side
    166.85x = 66,479.37
  5. Step 5: Solve for x
    x = 66,479.37/166.85
  6. Step 6: Final answer
    x = 398.43

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.