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Finding the Third Proportional to 209.50 and 295.25

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Solution

The third proportional to 209.50 and 295.25 is: 416.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.50 : 295.25 = 295.25 : x
  2. Step 2: Convert to fraction form
    209.50/295.25 = 295.25/x
  3. Step 3: Cross multiply
    209.50x = 295.25 × 295.25
  4. Step 4: Simplify right side
    209.50x = 87,172.56
  5. Step 5: Solve for x
    x = 87,172.56/209.50
  6. Step 6: Final answer
    x = 416.10

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.