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Finding the Third Proportional to 596 and 659

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Solution

The third proportional to 596 and 659 is: 728.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    596 : 659 = 659 : x
  2. Step 2: Convert to fraction form
    596/659 = 659/x
  3. Step 3: Cross multiply
    596x = 659 × 659
  4. Step 4: Simplify right side
    596x = 434,281
  5. Step 5: Solve for x
    x = 434,281/596
  6. Step 6: Final answer
    x = 728.66

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.