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Finding the Third Proportional to 1,540 and 2,182

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Solution

The third proportional to 1,540 and 2,182 is: 3,091.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,540 : 2,182 = 2,182 : x
  2. Step 2: Convert to fraction form
    1,540/2,182 = 2,182/x
  3. Step 3: Cross multiply
    1,540x = 2,182 × 2,182
  4. Step 4: Simplify right side
    1,540x = 4,761,124
  5. Step 5: Solve for x
    x = 4,761,124/1,540
  6. Step 6: Final answer
    x = 3,091.64

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.