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Finding the Third Proportional to 1,823 and 2,382

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Solution

The third proportional to 1,823 and 2,382 is: 3,112.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,823 : 2,382 = 2,382 : x
  2. Step 2: Convert to fraction form
    1,823/2,382 = 2,382/x
  3. Step 3: Cross multiply
    1,823x = 2,382 × 2,382
  4. Step 4: Simplify right side
    1,823x = 5,673,924
  5. Step 5: Solve for x
    x = 5,673,924/1,823
  6. Step 6: Final answer
    x = 3,112.41

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.