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Finding the Third Proportional to 2,057 and 3,207

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Solution

The third proportional to 2,057 and 3,207 is: 4,999.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,057 : 3,207 = 3,207 : x
  2. Step 2: Convert to fraction form
    2,057/3,207 = 3,207/x
  3. Step 3: Cross multiply
    2,057x = 3,207 × 3,207
  4. Step 4: Simplify right side
    2,057x = 10,284,849
  5. Step 5: Solve for x
    x = 10,284,849/2,057
  6. Step 6: Final answer
    x = 4,999.93

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.