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Finding the Third Proportional to 259 and 512

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Solution

The third proportional to 259 and 512 is: 1,012.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    259 : 512 = 512 : x
  2. Step 2: Convert to fraction form
    259/512 = 512/x
  3. Step 3: Cross multiply
    259x = 512 × 512
  4. Step 4: Simplify right side
    259x = 262,144
  5. Step 5: Solve for x
    x = 262,144/259
  6. Step 6: Final answer
    x = 1,012.14

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Why These Related Problems?

These problems maintain the same ratio (1.98) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.