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Finding the Third Proportional to 105 and 219

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Solution

The third proportional to 105 and 219 is: 456.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    105 : 219 = 219 : x
  2. Step 2: Convert to fraction form
    105/219 = 219/x
  3. Step 3: Cross multiply
    105x = 219 × 219
  4. Step 4: Simplify right side
    105x = 47,961
  5. Step 5: Solve for x
    x = 47,961/105
  6. Step 6: Final answer
    x = 456.77

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.