Question

tickets for a school carnival cost $10 for adults and $5 for children . last saturdays carnival sold 170 tickets worth a total of $1200 . how many adults and how many children attend the carnival ?

Answer 1

So (a) stands for adult and (c) is for child.

10a+5c=1200(total cost)

a+c=170(for tickets sold)

There are 70 adult tickets and 100 child tickets.

Answer 2

100 children and 70 adult tickets were sold.

Explanation:

Let x represent number of adult tickets and y represent number of children tickets.

We have been given that tickets for a school carnival cost $10 for adults, so cost of x tickets would be
`10x`.

Since cost of each ticket for children is $5, so cost of y tickets would be
`5y`.

We are told that last Saturday carnival sold tickets worth a total of $1200. We can represent this information in an equation as:

`10x+5y=1200...(1)`

We are also told that number of total tickets sold was 170. We can represent this information in an equation as:

`x+y=170...(2)`

Now, we will use substitution method to solve system of linear equations. From equation (2), we will get:

`x=170-y`

Upon substituting
`x=170-y` in equation (1), we will get:

`10(170-y)+5y=1200`

`1700-10y+5y=1200`

`1700-5y=1200`

`1700-1700-5y=1200-1700`

`-5y=-500`

`(-5y)/(-5)=(-500)/(-5)`

`y=100`

Therefore, 100 children tickets were sold.

To find number of children tickets sole, we will substitute
`y=100` in equation (2).

`x+100=170`

`x+100-100=170-100`

`x=70`

Therefore, 70 adult tickets were sold.