At a banquet the ratio of the number of boys to the number of girls is 5: 3. halfway through the banquet 20 boys leave and the ratio becomes 5: 4. how many girls are at the banquet?

X=number of boys
y=number of girls.
we suggest this system of equations:
x/y=5/3                 ⇒x=5y/3
(x-20)/y=5/4
We solve this problem by substituion method.

(5y/3 - 20)/y=5/4
4(5y/3 - 20)=5y
20y/3  -80=5y
least common multiple= 3
20y-240=15y
20y-15y=240
5y=240
y=240/5=48

x=5y/3
x=5*48/3=80

there are 48 girls at the banquet.