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Finding the Third Proportional to 106 and 170

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Solution

The third proportional to 106 and 170 is: 272.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 170 = 170 : x
  2. Step 2: Convert to fraction form
    106/170 = 170/x
  3. Step 3: Cross multiply
    106x = 170 × 170
  4. Step 4: Simplify right side
    106x = 28,900
  5. Step 5: Solve for x
    x = 28,900/106
  6. Step 6: Final answer
    x = 272.64

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.