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 ?

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.

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ApusApus ApusApus · Answer 2 · 2019-08-13T02:11:34-04:00

Answer:

100 children and 70 adult tickets were sold.

Step-by-step 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 @@MATH_TOKEN_0@@.

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:

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

$1700-10y+5y=1200$

$1700-5y=1200$

$1700-1700-5y=1200-1700$

$-5y=-500$

$\frac{-5y}{-5}=\frac{-500}{-5}$

$y=100$

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.