Question

If the number of $8 child tickets is 17 less than 3 times the number of $12 adult tickets and the theater took in $584, how many of each ticket were sold?

Answer 1

Number of child tickets sold = 43

Number of adult tickets sold = 20

Explanation:

Let the number of child ticket be c and number of adult ticket be a,

Given that the number of $8 child tickets is 17 less than 3 times the number of $12 adult tickets,

c = 3a - 17

3a - c = 17 ----------------------eqn 1

The theater received $584

That is

8 c + 12 a = 584 ----------------------eqn 2

eqn 2 /4

2 c + 3 a = 146 ----------------------eqn 3

eqn 3 - eqn 1 gives

2 c + 3 a - (3a - c) = 146 - 17

3 c = 129

c = 43

Substituting in eqn 1

3 x a - 43 = 17

3a = 60

a = 20

Number of child tickets sold = 43

Number of adult tickets sold = 20

Answer 2

The number of child tickets sold was 43 and the number of adult tickets sold was 20

Explanation:

Let

x ----> the number of child tickets sold

y ----> the number of adult tickets sold

we know that

`x=3y-17` -----> equation A

`8x+12y=584` ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (43,20)

see the attached figure

therefore

The number of child tickets sold was 43 and the number of adult tickets sold was 20