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.
