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Finding the Third Proportional to 2,974 and 6,823

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Solution

The third proportional to 2,974 and 6,823 is: 15,653.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,974 : 6,823 = 6,823 : x
  2. Step 2: Convert to fraction form
    2,974/6,823 = 6,823/x
  3. Step 3: Cross multiply
    2,974x = 6,823 × 6,823
  4. Step 4: Simplify right side
    2,974x = 46,553,329
  5. Step 5: Solve for x
    x = 46,553,329/2,974
  6. Step 6: Final answer
    x = 15,653.44

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Why These Related Problems?

These problems maintain the same ratio (2.29) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.