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Finding the Third Proportional to 422 and 464.50

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Solution

The third proportional to 422 and 464.50 is: 511.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    422 : 464.50 = 464.50 : x
  2. Step 2: Convert to fraction form
    422/464.50 = 464.50/x
  3. Step 3: Cross multiply
    422x = 464.50 × 464.50
  4. Step 4: Simplify right side
    422x = 215,760.25
  5. Step 5: Solve for x
    x = 215,760.25/422
  6. Step 6: Final answer
    x = 511.28

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.