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Finding the Third Proportional to 1,264 and 2,678

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Solution

The third proportional to 1,264 and 2,678 is: 5,673.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,264 : 2,678 = 2,678 : x
  2. Step 2: Convert to fraction form
    1,264/2,678 = 2,678/x
  3. Step 3: Cross multiply
    1,264x = 2,678 × 2,678
  4. Step 4: Simplify right side
    1,264x = 7,171,684
  5. Step 5: Solve for x
    x = 7,171,684/1,264
  6. Step 6: Final answer
    x = 5,673.80

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.