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Finding the Third Proportional to 1,097 and 2,374

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Solution

The third proportional to 1,097 and 2,374 is: 5,137.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,097 : 2,374 = 2,374 : x
  2. Step 2: Convert to fraction form
    1,097/2,374 = 2,374/x
  3. Step 3: Cross multiply
    1,097x = 2,374 × 2,374
  4. Step 4: Simplify right side
    1,097x = 5,635,876
  5. Step 5: Solve for x
    x = 5,635,876/1,097
  6. Step 6: Final answer
    x = 5,137.54

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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.