Question

You and your friend are selling tickets to a charity event. You sell 11 adult tickets and 8 student tickets for $158. Your friend sells 5 adult tickets and 17 student tickets for $152. What is the cost of a student ticket?

Answer 1

Hi, hope this helps :)

Answer 2

So what we have to do to solve this problem is to write down those values in 2 equations (one that represents what you sold and the other what your friend sold) compare them and find how much each ticket is worth.
First equation : 11x + 8y = 158
Where x = how much each adult ticket is
and y = how much each student ticket is

The second equation is : 5x + 17y = 152

Using the method of substitution , we can compare each equation side by side:
11x + 8y = 158
5x + 17y = 152
Now we need to set one of the variables of both equations so they are equal:
11(5)x + 8(5) = 158(5)
5(11)x + 17(11)x = 152(11)

55x + 40y = 790
55x + 187y = 1672

Then we subtract the second equation by the first one

55x-55x + 187y - 40y = 1672 - 790
147y = 882
y = 6
The we apply y to one of the equations to discover x :
11x + 8y = 158
11x + 8(6) = 158
11x + 48 = 158
11x = 110
x = 10

So the awnser is :
Each adult ticket (x) is $10
And each student ticket (y) is $8
I hope you understood my explanation,