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Finding the Third Proportional to 306.75 and 414.19

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Solution

The third proportional to 306.75 and 414.19 is: 559.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    306.75 : 414.19 = 414.19 : x
  2. Step 2: Convert to fraction form
    306.75/414.19 = 414.19/x
  3. Step 3: Cross multiply
    306.75x = 414.19 × 414.19
  4. Step 4: Simplify right side
    306.75x = 171,551.29
  5. Step 5: Solve for x
    x = 171,551.29/306.75
  6. Step 6: Final answer
    x = 559.25

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.