Maria bought seven boxes. a week later half of all her boxes were destroyed in a fire. there are now only 22 boxes left. with how many did she start?

Maria started with 37 boxes.

Given:
7 boxes bought
half of the boxes were destroyed in the fire.
22 boxes left

Find the beginning number of boxes. 
Let x be the beginning number of boxes.

(x + 7)/2 = 22

2((x+7)/2) = 2(22)
x + 7 = 44
x = 44 - 7
x = 37

To check:
x + 7 = 37 + 7 = 44
44 * 1/2 = 22
22 = 22