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Finding the Third Proportional to 1,378 and 1,678

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Solution

The third proportional to 1,378 and 1,678 is: 2,043.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,378 : 1,678 = 1,678 : x
  2. Step 2: Convert to fraction form
    1,378/1,678 = 1,678/x
  3. Step 3: Cross multiply
    1,378x = 1,678 × 1,678
  4. Step 4: Simplify right side
    1,378x = 2,815,684
  5. Step 5: Solve for x
    x = 2,815,684/1,378
  6. Step 6: Final answer
    x = 2,043.31

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.