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Finding the Third Proportional to 106.69 and 224.06

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Solution

The third proportional to 106.69 and 224.06 is: 470.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.69 : 224.06 = 224.06 : x
  2. Step 2: Convert to fraction form
    106.69/224.06 = 224.06/x
  3. Step 3: Cross multiply
    106.69x = 224.06 × 224.06
  4. Step 4: Simplify right side
    106.69x = 50,204.00
  5. Step 5: Solve for x
    x = 50,204.00/106.69
  6. Step 6: Final answer
    x = 470.57

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.