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

So start with the equation:

G/3 = B/5 [you know this because it says that the ratio of boys to girls is 5:3]

5G = 3B [Basic algebra]

5G = 4 (B-20)

If you are wondering where i got the B-20, its because you start with some number of boys (B), and then lose 20, so your new number of boys is (B-20)

Now you have a system of equations and can solve:

By substitution:

5G = 4 (B-20)

3B = 4 (B-20) [because remember that 5G = 3B]

B = 80

And since B = 80 and 5G = 3B,

G = 3 (80) / 5

G = 48

So you have 48 girls at the banquet