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Finding the Third Proportional to 106 and 239

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Solution

The third proportional to 106 and 239 is: 538.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 239 = 239 : x
  2. Step 2: Convert to fraction form
    106/239 = 239/x
  3. Step 3: Cross multiply
    106x = 239 × 239
  4. Step 4: Simplify right side
    106x = 57,121
  5. Step 5: Solve for x
    x = 57,121/106
  6. Step 6: Final answer
    x = 538.88

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Why These Related Problems?

These problems maintain the same ratio (2.25) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.