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Finding the Third Proportional to 414.75 and 678.75

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Solution

The third proportional to 414.75 and 678.75 is: 1,110.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.75 : 678.75 = 678.75 : x
  2. Step 2: Convert to fraction form
    414.75/678.75 = 678.75/x
  3. Step 3: Cross multiply
    414.75x = 678.75 × 678.75
  4. Step 4: Simplify right side
    414.75x = 460,701.56
  5. Step 5: Solve for x
    x = 460,701.56/414.75
  6. Step 6: Final answer
    x = 1,110.79

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.