Let x=gallons of 80% solution to be mixed
x+80=gallons go final 70% mixture
..
80%*x+30%*80=70%*(x+80)
.8x+24=.7x+56
.1x=32
x=320
gallons of 80% solution to be mixed=320
Think of it as two rectangular prisms next to each other, and find the volume of each one separately.
The big one on the left has a volume of 4 * 12 * 6, or 288.
The smaller one on the right has a volume of 2 * 6 * 6, or 72.
288 + 72 = 360. 360 cubic feet of water are needed.
X shortest piece
X+6 middle piece
X+8 longest piece
Add them
3x+14=56
3x=42
X=42/3=14
