On Tuesday Shanice bought five hats.On Wednesday half of all the hats that she had were destroyed.On Thursday there were only 17 left.How many Did she have on Monday.

From the given, we can setup an equation given by the two equations: (1) Number of hats on Monday, x, and 5 new hats bought on Tuesday is equal to total number of hats, h x+5 =h (2) Half of the hats is equal to 17 \frac{1}{2}h=17 We can get x by substituting equation (1) into (2): \frac{1}{2}\left(x+5\right)=17\xrightarrow{}x+5=34\xrightarrow{}x=34-5=29 Answer: 29 hats on Monday