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Finding the Third Proportional to 6,197 and 12,823

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Solution

The third proportional to 6,197 and 12,823 is: 26,533.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,197 : 12,823 = 12,823 : x
  2. Step 2: Convert to fraction form
    6,197/12,823 = 12,823/x
  3. Step 3: Cross multiply
    6,197x = 12,823 × 12,823
  4. Step 4: Simplify right side
    6,197x = 164,429,329
  5. Step 5: Solve for x
    x = 164,429,329/6,197
  6. Step 6: Final answer
    x = 26,533.70

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.