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Finding the Third Proportional to 1,830 and 3,971

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Solution

The third proportional to 1,830 and 3,971 is: 8,616.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,830 : 3,971 = 3,971 : x
  2. Step 2: Convert to fraction form
    1,830/3,971 = 3,971/x
  3. Step 3: Cross multiply
    1,830x = 3,971 × 3,971
  4. Step 4: Simplify right side
    1,830x = 15,768,841
  5. Step 5: Solve for x
    x = 15,768,841/1,830
  6. Step 6: Final answer
    x = 8,616.85

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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.