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Finding the Third Proportional to 2,586 and 2,838

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Solution

The third proportional to 2,586 and 2,838 is: 3,114.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,586 : 2,838 = 2,838 : x
  2. Step 2: Convert to fraction form
    2,586/2,838 = 2,838/x
  3. Step 3: Cross multiply
    2,586x = 2,838 × 2,838
  4. Step 4: Simplify right side
    2,586x = 8,054,244
  5. Step 5: Solve for x
    x = 8,054,244/2,586
  6. Step 6: Final answer
    x = 3,114.56

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.