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?

Shanice have 29 hats on Monday

Solution:

Given that  

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.

Let’s assume number of hats with Shanice on Monday be represented by variable "x"

As on Tuesday she bought five hats , so number of hats on Tuesday = x + 5

As On Wednesday half of all the hats that she had were destroyed , so half of all the hats on Tuesday were destroyed and half are remaining on thursday.

So remaining hats on Thursday = of number of hats on Tuesday

But its given remaining hats on Thursday = 17

Solving above expression for "x"

=> x = 34 – 5 = 29

As x represents number of hats with her on Mondays

Hence Shanice have 29 hats on Monday