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Finding the Third Proportional to 259 and 423

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Solution

The third proportional to 259 and 423 is: 690.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    259 : 423 = 423 : x
  2. Step 2: Convert to fraction form
    259/423 = 423/x
  3. Step 3: Cross multiply
    259x = 423 × 423
  4. Step 4: Simplify right side
    259x = 178,929
  5. Step 5: Solve for x
    x = 178,929/259
  6. Step 6: Final answer
    x = 690.85

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.