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Finding the Third Proportional to 2,056 and 4,196

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Solution

The third proportional to 2,056 and 4,196 is: 8,563.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,056 : 4,196 = 4,196 : x
  2. Step 2: Convert to fraction form
    2,056/4,196 = 4,196/x
  3. Step 3: Cross multiply
    2,056x = 4,196 × 4,196
  4. Step 4: Simplify right side
    2,056x = 17,606,416
  5. Step 5: Solve for x
    x = 17,606,416/2,056
  6. Step 6: Final answer
    x = 8,563.43

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.