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Finding the Third Proportional to 1,977 and 3,678

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Solution

The third proportional to 1,977 and 3,678 is: 6,842.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,977 : 3,678 = 3,678 : x
  2. Step 2: Convert to fraction form
    1,977/3,678 = 3,678/x
  3. Step 3: Cross multiply
    1,977x = 3,678 × 3,678
  4. Step 4: Simplify right side
    1,977x = 13,527,684
  5. Step 5: Solve for x
    x = 13,527,684/1,977
  6. Step 6: Final answer
    x = 6,842.53

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.