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Finding the Third Proportional to 853 and 1,199

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Solution

The third proportional to 853 and 1,199 is: 1,685.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    853 : 1,199 = 1,199 : x
  2. Step 2: Convert to fraction form
    853/1,199 = 1,199/x
  3. Step 3: Cross multiply
    853x = 1,199 × 1,199
  4. Step 4: Simplify right side
    853x = 1,437,601
  5. Step 5: Solve for x
    x = 1,437,601/853
  6. Step 6: Final answer
    x = 1,685.35

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.