Question

In a cinema hall a total of 215 tickets were sold. Some were sold at $8 and others at $12. If the total amount collected was 2180, how many $8 tickets were sold​

Answer 1

Answer: 100 tickets.

Explanation:

• Number of $8 tickets sold = x
• Number of $12 tickets sold = y

Set up two equations: one representing total amount sold and another representing total dollars earned.

`\left \{ {{x+y=215} \atop {8x+12y=2180}} \right.`

Rearrange x + y = 215 and find the value of x:

`x+y=215\\x=215-y`

Substitute it into the other equation and solve for y:

`8x+12y=2180\\8(215-y)+12y=2180\\1720-8y+12y=2180\\4y=2180-1720\\4y=460\\y=(460)/(4) =115`

Substitute in the y-value to the other expression to find x:

`x+y=215\\x+115=215\\x=215-115=100`

Therefore, they sold 100 of the $8 tickets.