9. The length and width of the rectangular bottom of Sabrina's new fish tank is twice the length and width of the rectangular bottom of her old tank. The area of the bottom of the new tank is 16 ft^2. The lengh of the old tank was 3 feet more than the width of the new tank.

a. Using F to represent the width of the old tank, write an equation to show the area of the new tank bottom

b. What was the width of the old tank?

c. What is the length of the new tank?

Ok so

F=old width

y=old legnth

z=new width

x=new legnth

we have

2F=z

2y=x

and area=16=lw=xz

and

y=3+z

subsitute 3+z for y

2 (3+z) = 6+2z=x

subsitute 6+2z for x in xz=16

(6+2z) (z) = 16

solve for z

distribute

2z^2+6z=16

divide 2

z^2+3z=8

subtract 8

z^2+3z-8=0

solve using quadratic formula

z=1.7

subsitute

zx=16

1.7*x=16

divide booth sides by 1.7

x=9.41

legnth (new) = 9.41

ok so we know that

doubleold=new so

old=1/2new

1.7=newW

oldW=1.7/2=0.85

so

equatn is

(6+2z) (z) = 16

z=width

b. width of old tank=0.85

c. legnth of new=9.41