How many Boys and Girls are there?

Let x be no of boys, thus no of girls is '12-x'.

700 x+(12-x) 500=8200

700 x-500 x=8200-6000

200*x=2200

x=11=no of boys

12-x=1=no of girls

only 1 option fulfill the total money......11 boys, 1 girl

11 boys+1 girl= $11 \times 700 +500=8200$ $.........[the answer]

b for boy, g for girl. b+g=12 (1), 700b+500g=8200 (2) => (1) multiply by 700 =>700b+700g=8400 (3) (3)-(1)=> 200g=200, g=1 Subs g=1 to (1) and b=11

Let x=8200 ie total amount

B be the no. Of boys and G be the no. Of girls

Amount by each - B = 700 G = 500

B+G=12..... (i)

700B+500G=8200.... (ii)

100 (7B+5G)=8200

7B+5G=82

From eq (i) B= 12-G

7(12-G)+5G=82

84-7G+5G=82

-2G=-2

From here no. Of girls = 1

No. Of boys = 12-G

12-1=11

If there are 11 Girls there would only be 6000 splited. For every girl you would trad for a boy it would add 200 to the splited total. Since there has to be splited 8200 there have to be 2200÷200=11 boys.