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Finding the Third Proportional to 106 and 221

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Solution

The third proportional to 106 and 221 is: 460.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 221 = 221 : x
  2. Step 2: Convert to fraction form
    106/221 = 221/x
  3. Step 3: Cross multiply
    106x = 221 × 221
  4. Step 4: Simplify right side
    106x = 48,841
  5. Step 5: Solve for x
    x = 48,841/106
  6. Step 6: Final answer
    x = 460.76

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.