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Finding the Third Proportional to 1,837 and 2,101

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Solution

The third proportional to 1,837 and 2,101 is: 2,402.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,837 : 2,101 = 2,101 : x
  2. Step 2: Convert to fraction form
    1,837/2,101 = 2,101/x
  3. Step 3: Cross multiply
    1,837x = 2,101 × 2,101
  4. Step 4: Simplify right side
    1,837x = 4,414,201
  5. Step 5: Solve for x
    x = 4,414,201/1,837
  6. Step 6: Final answer
    x = 2,402.94

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.