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Finding the Third Proportional to 259 and 424

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Solution

The third proportional to 259 and 424 is: 694.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    259 : 424 = 424 : x
  2. Step 2: Convert to fraction form
    259/424 = 424/x
  3. Step 3: Cross multiply
    259x = 424 × 424
  4. Step 4: Simplify right side
    259x = 179,776
  5. Step 5: Solve for x
    x = 179,776/259
  6. Step 6: Final answer
    x = 694.12

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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.