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Finding the Third Proportional to 231.47 and 419.06

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Solution

The third proportional to 231.47 and 419.06 is: 758.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    231.47 : 419.06 = 419.06 : x
  2. Step 2: Convert to fraction form
    231.47/419.06 = 419.06/x
  3. Step 3: Cross multiply
    231.47x = 419.06 × 419.06
  4. Step 4: Simplify right side
    231.47x = 175,613.38
  5. Step 5: Solve for x
    x = 175,613.38/231.47
  6. Step 6: Final answer
    x = 758.69

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Why These Related Problems?

These problems maintain the same ratio (1.81) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.