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Finding the Third Proportional to 1,205 and 2,569

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Solution

The third proportional to 1,205 and 2,569 is: 5,476.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,205 : 2,569 = 2,569 : x
  2. Step 2: Convert to fraction form
    1,205/2,569 = 2,569/x
  3. Step 3: Cross multiply
    1,205x = 2,569 × 2,569
  4. Step 4: Simplify right side
    1,205x = 6,599,761
  5. Step 5: Solve for x
    x = 6,599,761/1,205
  6. Step 6: Final answer
    x = 5,476.98

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.