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Finding the Third Proportional to 412 and 449.50

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Solution

The third proportional to 412 and 449.50 is: 490.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    412 : 449.50 = 449.50 : x
  2. Step 2: Convert to fraction form
    412/449.50 = 449.50/x
  3. Step 3: Cross multiply
    412x = 449.50 × 449.50
  4. Step 4: Simplify right side
    412x = 202,050.25
  5. Step 5: Solve for x
    x = 202,050.25/412
  6. Step 6: Final answer
    x = 490.41

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.