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Finding the Third Proportional to 1,678 and 2,007

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Solution

The third proportional to 1,678 and 2,007 is: 2,400.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,678 : 2,007 = 2,007 : x
  2. Step 2: Convert to fraction form
    1,678/2,007 = 2,007/x
  3. Step 3: Cross multiply
    1,678x = 2,007 × 2,007
  4. Step 4: Simplify right side
    1,678x = 4,028,049
  5. Step 5: Solve for x
    x = 4,028,049/1,678
  6. Step 6: Final answer
    x = 2,400.51

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.