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Finding the Third Proportional to 2,419 and 3,649

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Solution

The third proportional to 2,419 and 3,649 is: 5,504.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,419 : 3,649 = 3,649 : x
  2. Step 2: Convert to fraction form
    2,419/3,649 = 3,649/x
  3. Step 3: Cross multiply
    2,419x = 3,649 × 3,649
  4. Step 4: Simplify right side
    2,419x = 13,315,201
  5. Step 5: Solve for x
    x = 13,315,201/2,419
  6. Step 6: Final answer
    x = 5,504.42

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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.