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Finding the Third Proportional to 410 and 506

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Solution

The third proportional to 410 and 506 is: 624.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    410 : 506 = 506 : x
  2. Step 2: Convert to fraction form
    410/506 = 506/x
  3. Step 3: Cross multiply
    410x = 506 × 506
  4. Step 4: Simplify right side
    410x = 256,036
  5. Step 5: Solve for x
    x = 256,036/410
  6. Step 6: Final answer
    x = 624.48

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Why These Related Problems?

These problems maintain the same ratio (1.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.