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Finding the Third Proportional to 232 and 406.75

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Solution

The third proportional to 232 and 406.75 is: 713.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    232 : 406.75 = 406.75 : x
  2. Step 2: Convert to fraction form
    232/406.75 = 406.75/x
  3. Step 3: Cross multiply
    232x = 406.75 × 406.75
  4. Step 4: Simplify right side
    232x = 165,445.56
  5. Step 5: Solve for x
    x = 165,445.56/232
  6. Step 6: Final answer
    x = 713.13

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Why These Related Problems?

These problems maintain the same ratio (1.75) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.