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Finding the Third Proportional to 2,197 and 3,498

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Solution

The third proportional to 2,197 and 3,498 is: 5,569.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,197 : 3,498 = 3,498 : x
  2. Step 2: Convert to fraction form
    2,197/3,498 = 3,498/x
  3. Step 3: Cross multiply
    2,197x = 3,498 × 3,498
  4. Step 4: Simplify right side
    2,197x = 12,236,004
  5. Step 5: Solve for x
    x = 12,236,004/2,197
  6. Step 6: Final answer
    x = 5,569.41

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.