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Finding the Third Proportional to 232 and 257

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Solution

The third proportional to 232 and 257 is: 284.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    232 : 257 = 257 : x
  2. Step 2: Convert to fraction form
    232/257 = 257/x
  3. Step 3: Cross multiply
    232x = 257 × 257
  4. Step 4: Simplify right side
    232x = 66,049
  5. Step 5: Solve for x
    x = 66,049/232
  6. Step 6: Final answer
    x = 284.69

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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.