Assuming that both measurements are the areas, you have 150yds^2 of carpet to cover y rooms with each room needing 12 3/4^2 of carpet.
(If it confuses you, ignore the ^2 because it helps me understand what I'm doing)
For me, it's easier to convert fractions to decimals. 12 3/4 = 12.75
So now you have this equation: 12.75 × y = 150
In algebra, you want to isolate the y, aka the unknown variable. To do so, you need to divide each side by 12.75.
12.75 × y = 150 ------------ ------ 12.75. 12.75
On the left, you can cross out the 12.75 because it's divided by itself, thereby making it 1. There's no need to have 1y, it's just y. On the other hand, you divide 150 by 12.75, which equals 11.7647059.
Now you might assume to round up this number, making it 12 rooms, but it simply doesn't work. You would have 11 complete rooms and one partially covered room. Therefore, your answer is y = 11 rooms.
