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Finding the Third Proportional to 257 and 421

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Solution

The third proportional to 257 and 421 is: 689.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    257 : 421 = 421 : x
  2. Step 2: Convert to fraction form
    257/421 = 421/x
  3. Step 3: Cross multiply
    257x = 421 × 421
  4. Step 4: Simplify right side
    257x = 177,241
  5. Step 5: Solve for x
    x = 177,241/257
  6. Step 6: Final answer
    x = 689.65

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.