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Finding the Third Proportional to 106.32 and 164.29

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Solution

The third proportional to 106.32 and 164.29 is: 253.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.32 : 164.29 = 164.29 : x
  2. Step 2: Convert to fraction form
    106.32/164.29 = 164.29/x
  3. Step 3: Cross multiply
    106.32x = 164.29 × 164.29
  4. Step 4: Simplify right side
    106.32x = 26,989.66
  5. Step 5: Solve for x
    x = 26,989.66/106.32
  6. Step 6: Final answer
    x = 253.85

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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.