problem simultaneous equations

Hey i need help, i dont know the working outs.

a shopkeeper sold his entire stock of shirts and ties in a sale for $10 000. The shirts were priced at 3 for $100 and the ties $20 each. if he had sold only half the shirts and two-thirds of the ties he would have received $6000. how many of each did he sell in the sale?

answer- 120 shirts and 300 ties

attempt.

shirts -x ties - y

x+y= 10 000

3x= $100

y=$20

if he had sold only half the shirts and two-thirds of the ties he would have received $6000 ?

shirts x/2 ties 2y/3 ?? so x/2 + 2y/3= 6000 ??

3- a party was organized for thirty people at which they could have either a hamburger or a pizza. if there was five times as many hamburgers as pizzas calculate the number of each.

x be hamburger, y be pizza

5x..

answer- 5 pizzas and 25 hamburgers

thankss