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Finding the Third Proportional to 407 and 449.75

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Solution

The third proportional to 407 and 449.75 is: 496.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    407 : 449.75 = 449.75 : x
  2. Step 2: Convert to fraction form
    407/449.75 = 449.75/x
  3. Step 3: Cross multiply
    407x = 449.75 × 449.75
  4. Step 4: Simplify right side
    407x = 202,275.06
  5. Step 5: Solve for x
    x = 202,275.06/407
  6. Step 6: Final answer
    x = 496.99

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.