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Finding the Third Proportional to 410 and 519.50

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Solution

The third proportional to 410 and 519.50 is: 658.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    410 : 519.50 = 519.50 : x
  2. Step 2: Convert to fraction form
    410/519.50 = 519.50/x
  3. Step 3: Cross multiply
    410x = 519.50 × 519.50
  4. Step 4: Simplify right side
    410x = 269,880.25
  5. Step 5: Solve for x
    x = 269,880.25/410
  6. Step 6: Final answer
    x = 658.24

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.