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Finding the Fourth Proportional to 513, 769.50 and 209

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Solution

The fourth proportional to 513, 769.50 and 209 is: 313.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    513 : 769.50 = 209 : x
  2. Step 2: Convert to fraction form
    513/769.50 = 209/x
  3. Step 3: Cross multiply
    513x = 769.50 × 209
  4. Step 4: Simplify right side
    513x = 160,825.50
  5. Step 5: Solve for x
    x = 160,825.50/513
  6. Step 6: Final answer
    x = 313.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.