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Finding the Third Proportional to 109 and 214.50

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Solution

The third proportional to 109 and 214.50 is: 422.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    109 : 214.50 = 214.50 : x
  2. Step 2: Convert to fraction form
    109/214.50 = 214.50/x
  3. Step 3: Cross multiply
    109x = 214.50 × 214.50
  4. Step 4: Simplify right side
    109x = 46,010.25
  5. Step 5: Solve for x
    x = 46,010.25/109
  6. Step 6: Final answer
    x = 422.11

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.