2x - 11
-9 + x
equate the equations
2x - 11 = -9 + x
bring like terms to one side
2x - 11 = -9 + x
- x +11 +11 - x
-11 and +11 cancels out
+x and -x cancels out
2x - x = 11 - 9
x = 2
Let width and length be x and y respectively.
Perimeter (32in) =2x+2y=> 16=x+y => y=16-x
Area, A = xy = x(16-x) = 16x-x^2
The function to maximize is area: A=16 x-x^2
For maximum area, the first derivative of A =0 => A'=16-2x =0
Solving for x: 16-2x=0 =>2x=16 => x=8 in
And therefore, y=16-8 = 8 in
There are 29 quarts of fruit punch in 7.25 gallons of fruit punch.