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Finding the Third Proportional to 523 and 599

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Solution

The third proportional to 523 and 599 is: 686.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 599 = 599 : x
  2. Step 2: Convert to fraction form
    523/599 = 599/x
  3. Step 3: Cross multiply
    523x = 599 × 599
  4. Step 4: Simplify right side
    523x = 358,801
  5. Step 5: Solve for x
    x = 358,801/523
  6. Step 6: Final answer
    x = 686.04

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.