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Finding the Third Proportional to 1,209 and 1,805

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Solution

The third proportional to 1,209 and 1,805 is: 2,694.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,209 : 1,805 = 1,805 : x
  2. Step 2: Convert to fraction form
    1,209/1,805 = 1,805/x
  3. Step 3: Cross multiply
    1,209x = 1,805 × 1,805
  4. Step 4: Simplify right side
    1,209x = 3,258,025
  5. Step 5: Solve for x
    x = 3,258,025/1,209
  6. Step 6: Final answer
    x = 2,694.81

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.