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Finding the Third Proportional to 420 and 462.75

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Solution

The third proportional to 420 and 462.75 is: 509.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    420 : 462.75 = 462.75 : x
  2. Step 2: Convert to fraction form
    420/462.75 = 462.75/x
  3. Step 3: Cross multiply
    420x = 462.75 × 462.75
  4. Step 4: Simplify right side
    420x = 214,137.56
  5. Step 5: Solve for x
    x = 214,137.56/420
  6. Step 6: Final answer
    x = 509.85

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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.