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Finding the Fourth Proportional to 1,982.02, 2,972.49 and 827.50

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Solution

The fourth proportional to 1,982.02, 2,972.49 and 827.50 is: 1,241.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,982.02 : 2,972.49 = 827.50 : x
  2. Step 2: Convert to fraction form
    1,982.02/2,972.49 = 827.50/x
  3. Step 3: Cross multiply
    1,982.02x = 2,972.49 × 827.50
  4. Step 4: Simplify right side
    1,982.02x = 2,459,735.48
  5. Step 5: Solve for x
    x = 2,459,735.48/1,982.02
  6. Step 6: Final answer
    x = 1,241.02

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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.