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Finding the Third Proportional to 384.75 and 420.75

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Solution

The third proportional to 384.75 and 420.75 is: 460.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    384.75 : 420.75 = 420.75 : x
  2. Step 2: Convert to fraction form
    384.75/420.75 = 420.75/x
  3. Step 3: Cross multiply
    384.75x = 420.75 × 420.75
  4. Step 4: Simplify right side
    384.75x = 177,030.56
  5. Step 5: Solve for x
    x = 177,030.56/384.75
  6. Step 6: Final answer
    x = 460.12

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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.