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Finding the Third Proportional to 106.50 and 164.53

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Solution

The third proportional to 106.50 and 164.53 is: 254.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.50 : 164.53 = 164.53 : x
  2. Step 2: Convert to fraction form
    106.50/164.53 = 164.53/x
  3. Step 3: Cross multiply
    106.50x = 164.53 × 164.53
  4. Step 4: Simplify right side
    106.50x = 27,070.53
  5. Step 5: Solve for x
    x = 27,070.53/106.50
  6. Step 6: Final answer
    x = 254.18

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.