Answer to Question #25530 in Algebra for Yi Tong

Question

On the first day of the fun fair, there were 400 more boys than girls. On the second day, the number of boys increased by 30% and the number of girls increased by 70%. There were 2020 children on the second day. How many boys were there on the first day?

Answer 1

On the first day of the fun fair, there were 400 more boys than girls. On
the second day, the number of boys increased by 30% and the number of girls
increased by 70%. There were 2020 children on the second day. How many boys
were there on the first day?
Let's denote the number of boys and girls on the first day by B and G respectivly. As there were 400 more boys than girls on the first day, then
B = G + 400.(1)
On the second day:
1.3B + 1.7G = 2020.(2)
We've got a system of equations. Let's solve it. Substituting (1) into (2) we obtain:
(G + 400)·1.3 + 1.7G = 2020 ==>
1.3G + 1.3*400 + 1.7G = 2020 ==>
3G = 1500 ==> G = 500 ==> B = 500 + 400 = 900.
Therefore, there were 500 girls and 900 boys on the first day.