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Finding the Third Proportional to 1,106 and 2,164

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Solution

The third proportional to 1,106 and 2,164 is: 4,234.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106 : 2,164 = 2,164 : x
  2. Step 2: Convert to fraction form
    1,106/2,164 = 2,164/x
  3. Step 3: Cross multiply
    1,106x = 2,164 × 2,164
  4. Step 4: Simplify right side
    1,106x = 4,682,896
  5. Step 5: Solve for x
    x = 4,682,896/1,106
  6. Step 6: Final answer
    x = 4,234.08

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Why These Related Problems?

These problems maintain the same ratio (1.96) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.