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Finding the Third Proportional to 1,827 and 1,983

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Solution

The third proportional to 1,827 and 1,983 is: 2,152.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,827 : 1,983 = 1,983 : x
  2. Step 2: Convert to fraction form
    1,827/1,983 = 1,983/x
  3. Step 3: Cross multiply
    1,827x = 1,983 × 1,983
  4. Step 4: Simplify right side
    1,827x = 3,932,289
  5. Step 5: Solve for x
    x = 3,932,289/1,827
  6. Step 6: Final answer
    x = 2,152.32

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.