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Finding the Third Proportional to 257 and 423

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Solution

The third proportional to 257 and 423 is: 696.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    257 : 423 = 423 : x
  2. Step 2: Convert to fraction form
    257/423 = 423/x
  3. Step 3: Cross multiply
    257x = 423 × 423
  4. Step 4: Simplify right side
    257x = 178,929
  5. Step 5: Solve for x
    x = 178,929/257
  6. Step 6: Final answer
    x = 696.22

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Why These Related Problems?

These problems maintain the same ratio (1.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.