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Finding the Third Proportional to 420 and 464.50

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Solution

The third proportional to 420 and 464.50 is: 513.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    420 : 464.50 = 464.50 : x
  2. Step 2: Convert to fraction form
    420/464.50 = 464.50/x
  3. Step 3: Cross multiply
    420x = 464.50 × 464.50
  4. Step 4: Simplify right side
    420x = 215,760.25
  5. Step 5: Solve for x
    x = 215,760.25/420
  6. Step 6: Final answer
    x = 513.71

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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.