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Finding the Third Proportional to 2,049 and 3,101

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Solution

The third proportional to 2,049 and 3,101 is: 4,693.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,049 : 3,101 = 3,101 : x
  2. Step 2: Convert to fraction form
    2,049/3,101 = 3,101/x
  3. Step 3: Cross multiply
    2,049x = 3,101 × 3,101
  4. Step 4: Simplify right side
    2,049x = 9,616,201
  5. Step 5: Solve for x
    x = 9,616,201/2,049
  6. Step 6: Final answer
    x = 4,693.12

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.