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Finding the Third Proportional to 142.38 and 213.26

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Solution

The third proportional to 142.38 and 213.26 is: 319.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    142.38 : 213.26 = 213.26 : x
  2. Step 2: Convert to fraction form
    142.38/213.26 = 213.26/x
  3. Step 3: Cross multiply
    142.38x = 213.26 × 213.26
  4. Step 4: Simplify right side
    142.38x = 45,478.89
  5. Step 5: Solve for x
    x = 45,478.89/142.38
  6. Step 6: Final answer
    x = 319.41

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.