Step 1 :Let p represent the number of pens Shanice had on Monday. After buying 5 new pens on Tuesday, she had (p + 5) pens. On Wednesday, half of her pens were thrown away, so she had (p + 5)/2 pens left. On Thursday, she had 16 pens, so we can set up the following equation: \(\frac{p + 5}{2} = 16\)
Step 2 :To solve for p, we can multiply both sides of the equation by 2: \(p + 5 = 32\). Then, subtract 5 from both sides: \(p = 27\).
Step 3 :\(\boxed{27}\)