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Finding the Third Proportional to 420.75 and 459.56

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Solution

The third proportional to 420.75 and 459.56 is: 501.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    420.75 : 459.56 = 459.56 : x
  2. Step 2: Convert to fraction form
    420.75/459.56 = 459.56/x
  3. Step 3: Cross multiply
    420.75x = 459.56 × 459.56
  4. Step 4: Simplify right side
    420.75x = 211,197.69
  5. Step 5: Solve for x
    x = 211,197.69/420.75
  6. Step 6: Final answer
    x = 501.96

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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.