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Finding the Third Proportional to 414 and 549.25

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Solution

The third proportional to 414 and 549.25 is: 728.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 549.25 = 549.25 : x
  2. Step 2: Convert to fraction form
    414/549.25 = 549.25/x
  3. Step 3: Cross multiply
    414x = 549.25 × 549.25
  4. Step 4: Simplify right side
    414x = 301,675.56
  5. Step 5: Solve for x
    x = 301,675.56/414
  6. Step 6: Final answer
    x = 728.68

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.