Let
x-------> <span>the probability that a boy is chosen
B------> </span>number of boys in the debate team
G------> number of girls in the debate team<span>
we know that
B+G=20-----> G=20-B-----> equation 1
</span>probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2
t<span>he probability that a girl is chosen is 2/3 the probability that a boy is chosen
</span>probability that a girl is chosen=(2/3)*x
probability that a girl is chosen=G/20
(2/3)*x=G/20-----> equation 3
substitute equation 1 in equation 3
(2/3)*x=[20-B]/20----> equation 4
resolve the equations system
x=B/20
(2/3)*x=[20-B]/20
using a graph tool
see the attached figure
the solution is
x=0.6
B=12
G=20-12-----> G=8
number of boys in the debate team is 12
number of girls in the debate team is 8
the probability that a boy is chosen is 0.6 ----> 60%
the probability that a girl is chosen is 0.6*(2/3)----> 0.4---> 40%
the answer isnumber of girls in the debate team is 8
be the length of the rectangle and 
be the width. In the problem it is given that 
. It is also given that the area 
. Substituting in the length in terms of width, we have 
. Using the zero product property, 
. Solving these we get the width 
. However, it doesn't make sense for the width to be negative, so the width must be 
. From that we can tell the length 
.
