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Finding the Third Proportional to 420.75 and 455.75

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Solution

The third proportional to 420.75 and 455.75 is: 493.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    420.75 : 455.75 = 455.75 : x
  2. Step 2: Convert to fraction form
    420.75/455.75 = 455.75/x
  3. Step 3: Cross multiply
    420.75x = 455.75 × 455.75
  4. Step 4: Simplify right side
    420.75x = 207,708.06
  5. Step 5: Solve for x
    x = 207,708.06/420.75
  6. Step 6: Final answer
    x = 493.66

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.