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Finding the Third Proportional to 380.50 and 821.75

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Solution

The third proportional to 380.50 and 821.75 is: 1,774.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    380.50 : 821.75 = 821.75 : x
  2. Step 2: Convert to fraction form
    380.50/821.75 = 821.75/x
  3. Step 3: Cross multiply
    380.50x = 821.75 × 821.75
  4. Step 4: Simplify right side
    380.50x = 675,273.06
  5. Step 5: Solve for x
    x = 675,273.06/380.50
  6. Step 6: Final answer
    x = 1,774.70

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.