Question

650 tickets were sold for a game for a total of $1,200.00. if adult tickets sold for $2.00 and children's tickets sold for $1.50, how many of each kind of ticket were sold?

Answer 1

450 adult tickets and 200 children tickets were sold

Explanation:

let a be number of adult tickets and c the number of child tickets sold, then

a + c = 650 → (1) ( based on total number of tickets sold )

2a + 1.5c = 1200 → (2) ( based on ticket sales )

multiplying (1) by - 2 and adding the result to (2) will eliminate a

- 2a - 2c = - 1300 → (3)

add (2) and (3) term by term to eliminate a

(2a - 2a) + (1.5c - 2c) = 1200 - 1300

0 - 0.5c = - 100

- 0.5c = - 100 ( divide both sides by - 0.5 )

`(-0.5)/(-0.5)` c =
`(-100)/(-0.5)` , that is

c = 200

substitute c = 200 into (1) and solve for a

a + 200 = 650 ( subtract 200 from both sides )

a = 450

then

450 adult tickets and 200 children's tickets were sold