Question

A school is selling tickets to a drama performance. On the first day of ticket sales the school sold 3 adult tickets and 1 child ticket for a total of $38. On the second day, the school sold 3 adult tickets and 2 child tickets for a total of $52.

Which of the following system of linear equations could model this situation?

Answer 1

System of linear equations

`\left\{\begin{matrix} 3a+c=38 \\\\ 3a+2c=52 \end{matrix}\right.`

a: adult ticket price and c: child ticket price

Explanation:

This system of equations can be used to find the price of the adult and child tickets.

We have two equations (one for each day) and two unknowns (adult ticket price and child ticket price).

Let a: adult ticket price and c: child ticket price,

we have for the first day that 3 adult tickets and 1 child ticket adds $38:

`3a+1c=38`

and for the second day we have that 2 adult tickets and 2 child tickets adds $52:

`3a+2c=52`

If we write this as a system of equations, we have:

`\left\{\begin{matrix} 3a+c=38 \\\\ 3a+2c=52 \end{matrix}\right.`