Question

The school that Jennifer goes to is selling tickets to a play. On the first day of ticket sales the

school sold 3 adult tickets and 12 child tickets for a total of $141. The school took in $197 on the
second day by selling 13 adult tickets and 6 child tickets. What is the price each of one adult
ticket and one child ticket?

Answer 1

Adult ticket = $11

Children ticket = $9

Explanation:

Let the price of adult tickets be x and let the price of children's ticket be y

For the first day, the equation of sales can be put as

3x + 12y = 141..........1

For the second day, the equation of sales can be put as:

13x + 6y = 197............2

We then take these two equations together and solve simultaneously.

3x + 12y = 141.......1

13x + 6y = 197........2

Solving by elimination method, we Multiply through equation 1 by 13 and multiply through equation 2 by 3.

39x + 156y = 1833.........3

39x + 18y = 591..............4

Then subtract equation 4 from equation 3

138y =1242

y = 9

Substitute "y=9" into equation 1 to find x

3x + 12(9) =141

3x + 108 = 141

3x = 141 - 108

3x = 33

x = 11

Hence,

Price of adult ticket = $11

Price of children ticket = $9