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Finding the Third Proportional to 414.75 and 764.53

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Solution

The third proportional to 414.75 and 764.53 is: 1,409.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.75 : 764.53 = 764.53 : x
  2. Step 2: Convert to fraction form
    414.75/764.53 = 764.53/x
  3. Step 3: Cross multiply
    414.75x = 764.53 × 764.53
  4. Step 4: Simplify right side
    414.75x = 584,508.03
  5. Step 5: Solve for x
    x = 584,508.03/414.75
  6. Step 6: Final answer
    x = 1,409.30

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Why These Related Problems?

These problems maintain the same ratio (1.84) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.