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Finding the Third Proportional to 106 and 224

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Solution

The third proportional to 106 and 224 is: 473.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 224 = 224 : x
  2. Step 2: Convert to fraction form
    106/224 = 224/x
  3. Step 3: Cross multiply
    106x = 224 × 224
  4. Step 4: Simplify right side
    106x = 50,176
  5. Step 5: Solve for x
    x = 50,176/106
  6. Step 6: Final answer
    x = 473.36

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.