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Finding the Third Proportional to 378.75 and 420.56

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Solution

The third proportional to 378.75 and 420.56 is: 466.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    378.75 : 420.56 = 420.56 : x
  2. Step 2: Convert to fraction form
    378.75/420.56 = 420.56/x
  3. Step 3: Cross multiply
    378.75x = 420.56 × 420.56
  4. Step 4: Simplify right side
    378.75x = 176,872.82
  5. Step 5: Solve for x
    x = 176,872.82/378.75
  6. Step 6: Final answer
    x = 466.99

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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.