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Finding the Third Proportional to 2,022 and 4,157

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Solution

The third proportional to 2,022 and 4,157 is: 8,546.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,022 : 4,157 = 4,157 : x
  2. Step 2: Convert to fraction form
    2,022/4,157 = 4,157/x
  3. Step 3: Cross multiply
    2,022x = 4,157 × 4,157
  4. Step 4: Simplify right side
    2,022x = 17,280,649
  5. Step 5: Solve for x
    x = 17,280,649/2,022
  6. Step 6: Final answer
    x = 8,546.32

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.