William bought some tickets to see his favorite singer. He bought some adult tickets and some children's tickets, for a total of 15 tickets. The adult tickets cost $30 per ticket, and the children's tickets cost $20 per ticket. If he spent a total of $270, then how many adult and children's tickets did he buy

Set x as adult tickets.

Set y as children's tickets.

x + y = 15

30x + 20y = 270

Solve for x in the first equation.

x + y = 15

x = 15 - y

Plug this into the second equation.

30x + 20y = 270

30 (15 - y) + 20y = 270

450 - 30y + 20y = 270

450 - 10y = 270

-10y = - 180

y = 18

If there is 18 childrens tickets, there should be - 3 adult tickets.

This is impossible, and this impossible answer occured because the question is written wrong.

There are a total of 15 tickets

The smallest costing ticket is the childrens ticket, which costs 20$.

If he only bought children tickets, this would be 20x15 which is 300$.

300$ is over 270$, which makes the question impossible.