How many blue rectangles there are? Blue and red rectangles are drawn on a blackboard. Exactly 7 of the rectangles are squares. There are 3 
red rectangles more than blue squares. There are 2 red squares more than blue rectangles. How many blue rectangles are there?

Let $bs$,$bn$,$rs$, and $rn$ denote the number of blue squares, blue rectangles that are not squares, red squares and red rectangles that are not squares respectively, where each must be a non negative integer.
Then, the given conditions give the following equations:
$$rs+bs=7$$
$$bs+3=rs+rn$$
$$bs+bn+2=rs$$
Using the first and the third equation to eliminate $rs$, we get
$$bs+bn+2=7-bs$$
or $$2bs+bn=5$$
Now,
$$rs=7-bs$$
$$rs+rn=bs+3\ge rs$$
Thus
$$bs+3\ge 7-bs$$
$$bs\ge 2$$
For $bs$ and $bn$ to be non negative integers, in $2bs+bn=5$, we have $bs\le2$
Thus 
$$bs=2$$
$$bn=5-2bs=1$$
Also $rs=5$ and $rn=0$
The number of blue rectangles is $bs+bn=3$
