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

Answer: there are 48 girls at the banquet.