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Finding the Third Proportional to 283,972 and 431,142

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Solution

The third proportional to 283,972 and 431,142 is: 654,583.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    283,972 : 431,142 = 431,142 : x
  2. Step 2: Convert to fraction form
    283,972/431,142 = 431,142/x
  3. Step 3: Cross multiply
    283,972x = 431,142 × 431,142
  4. Step 4: Simplify right side
    283,972x = 185,883,424,164
  5. Step 5: Solve for x
    x = 185,883,424,164/283,972
  6. Step 6: Final answer
    x = 654,583.64

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.