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Finding the Third Proportional to 513 and 583.50

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Solution

The third proportional to 513 and 583.50 is: 663.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    513 : 583.50 = 583.50 : x
  2. Step 2: Convert to fraction form
    513/583.50 = 583.50/x
  3. Step 3: Cross multiply
    513x = 583.50 × 583.50
  4. Step 4: Simplify right side
    513x = 340,472.25
  5. Step 5: Solve for x
    x = 340,472.25/513
  6. Step 6: Final answer
    x = 663.69

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.