Question

The movie theater took in $1,220 one Monday night. The number of $7 child tickets was 10 more than twice the number of $9 adult tickets. How many of each were sold?

Answer 1

Answer: 110 child tickets and 50 adult tickets were sold.

Explanation:

Let x be the number of child tickets and y be the number of adult tickets.

then, According to the given information, we have

`7x+9y=1220------------(1)\\\\x=10+2y----------(2)`

Substitute the value of x from (2) in (1), we get

`7((10+2y))+9y=1220\\\\\Rightarrow\ 70+14y+9y=1220\\\\\Rightarrow\ 23y=1220-70\\\\\Rightarrow\ 23y=1150\\\\\Rightarrow\ y=(1150)/(23)=50`

Now, put the value of y in (2), we get

`x=10+2(50)=110`

Hence, 110 child tickets and 50 adult tickets were sold.