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Finding the Third Proportional to 1,194 and 1,299

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Solution

The third proportional to 1,194 and 1,299 is: 1,413.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,194 : 1,299 = 1,299 : x
  2. Step 2: Convert to fraction form
    1,194/1,299 = 1,299/x
  3. Step 3: Cross multiply
    1,194x = 1,299 × 1,299
  4. Step 4: Simplify right side
    1,194x = 1,687,401
  5. Step 5: Solve for x
    x = 1,687,401/1,194
  6. Step 6: Final answer
    x = 1,413.23

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.