Question

A theater wants to take in 2000 dollars for a certain matinee. Children's tickets cost 5 dollars each and adult tickets cost 10 dollars each. If the theater has a maximum of 350 seats, write a system of equations that can be solved to determine the number of both children and adult tickets the theater can sell.

Answer 1

We have the following system of equations:

`\left \{ {5x + 10 y = 2.000 (1)} \atop {x + y = 350 (2)} \right.`

(2) = x = 350-y . Replace x in equation (1 )

=> 5(350-y)+10y=2000 => y = 241

Replace y=241 in equation (2 ) => x = 350-241 = 109

the number of both children and adult tickets the theater can sell.

Children tickets : 109

Adult tickets : 241

Explanation: