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Finding the Third Proportional to 1,830 and 3,978

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Solution

The third proportional to 1,830 and 3,978 is: 8,647.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,830 : 3,978 = 3,978 : x
  2. Step 2: Convert to fraction form
    1,830/3,978 = 3,978/x
  3. Step 3: Cross multiply
    1,830x = 3,978 × 3,978
  4. Step 4: Simplify right side
    1,830x = 15,824,484
  5. Step 5: Solve for x
    x = 15,824,484/1,830
  6. Step 6: Final answer
    x = 8,647.26

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.