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Finding the Third Proportional to 821.75 and 1,197.38

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Solution

The third proportional to 821.75 and 1,197.38 is: 1,744.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    821.75 : 1,197.38 = 1,197.38 : x
  2. Step 2: Convert to fraction form
    821.75/1,197.38 = 1,197.38/x
  3. Step 3: Cross multiply
    821.75x = 1,197.38 × 1,197.38
  4. Step 4: Simplify right side
    821.75x = 1,433,706.89
  5. Step 5: Solve for x
    x = 1,433,706.89/821.75
  6. Step 6: Final answer
    x = 1,744.70

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.