Question

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?

Answer 1

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