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Finding the Third Proportional to 2,109 and 2,454

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Solution

The third proportional to 2,109 and 2,454 is: 2,855.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,109 : 2,454 = 2,454 : x
  2. Step 2: Convert to fraction form
    2,109/2,454 = 2,454/x
  3. Step 3: Cross multiply
    2,109x = 2,454 × 2,454
  4. Step 4: Simplify right side
    2,109x = 6,022,116
  5. Step 5: Solve for x
    x = 6,022,116/2,109
  6. Step 6: Final answer
    x = 2,855.44

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.