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Finding the Third Proportional to 106 and 164

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Solution

The third proportional to 106 and 164 is: 253.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 164 = 164 : x
  2. Step 2: Convert to fraction form
    106/164 = 164/x
  3. Step 3: Cross multiply
    106x = 164 × 164
  4. Step 4: Simplify right side
    106x = 26,896
  5. Step 5: Solve for x
    x = 26,896/106
  6. Step 6: Final answer
    x = 253.74

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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.