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Finding the Third Proportional to 257.34 and 409.64

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Solution

The third proportional to 257.34 and 409.64 is: 652.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    257.34 : 409.64 = 409.64 : x
  2. Step 2: Convert to fraction form
    257.34/409.64 = 409.64/x
  3. Step 3: Cross multiply
    257.34x = 409.64 × 409.64
  4. Step 4: Simplify right side
    257.34x = 167,805.44
  5. Step 5: Solve for x
    x = 167,805.44/257.34
  6. Step 6: Final answer
    x = 652.07

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.