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Finding the Third Proportional to 270.75 and 419.06

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Solution

The third proportional to 270.75 and 419.06 is: 648.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    270.75 : 419.06 = 419.06 : x
  2. Step 2: Convert to fraction form
    270.75/419.06 = 419.06/x
  3. Step 3: Cross multiply
    270.75x = 419.06 × 419.06
  4. Step 4: Simplify right side
    270.75x = 175,613.38
  5. Step 5: Solve for x
    x = 175,613.38/270.75
  6. Step 6: Final answer
    x = 648.62

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.