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Finding the Third Proportional to 1,830 and 2,831

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Solution

The third proportional to 1,830 and 2,831 is: 4,379.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,830 : 2,831 = 2,831 : x
  2. Step 2: Convert to fraction form
    1,830/2,831 = 2,831/x
  3. Step 3: Cross multiply
    1,830x = 2,831 × 2,831
  4. Step 4: Simplify right side
    1,830x = 8,014,561
  5. Step 5: Solve for x
    x = 8,014,561/1,830
  6. Step 6: Final answer
    x = 4,379.54

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.