how to solve this in two variable equation

Question

Each boy contributed rupees equal to the number of girls and each girl contributed rupees equal to the number of boys in a class of 60 students. if the total contribution thus collected is Rs 1600 how many boys are there in the class ?

Answer 1

b=# of boys

g=# of girls

b+g=60

bg+gb=1600

bg+bg=1600

2bg=1600

bg=1600/2

bg=800

from b+g=60 we have g=60-b

substitute

bg=800

b(60-b)=800

60b-b²=800

b²-60b+800=0

factor

(b-40)(b-20)=0

b-40=0

b=40

g=60-40

g=20

there could be 20 boys and 40 girls or 40 boys and 20 girls