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Finding the Third Proportional to 409.88 and 682.69

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Solution

The third proportional to 409.88 and 682.69 is: 1,137.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.88 : 682.69 = 682.69 : x
  2. Step 2: Convert to fraction form
    409.88/682.69 = 682.69/x
  3. Step 3: Cross multiply
    409.88x = 682.69 × 682.69
  4. Step 4: Simplify right side
    409.88x = 466,062.22
  5. Step 5: Solve for x
    x = 466,062.22/409.88
  6. Step 6: Final answer
    x = 1,137.08

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Why These Related Problems?

These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.