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Finding the Third Proportional to 1,586 and 2,531

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Solution

The third proportional to 1,586 and 2,531 is: 4,039.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,586 : 2,531 = 2,531 : x
  2. Step 2: Convert to fraction form
    1,586/2,531 = 2,531/x
  3. Step 3: Cross multiply
    1,586x = 2,531 × 2,531
  4. Step 4: Simplify right side
    1,586x = 6,405,961
  5. Step 5: Solve for x
    x = 6,405,961/1,586
  6. Step 6: Final answer
    x = 4,039.07

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.