I need help solving this problems by creating a system of equations

Question

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 6 senior citizen tickets and 3 child ticket for a total of $156. The school took in 88$ on there second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket by writing a system of equations and solving it.

Answer 1

1st concert: 6s + 3c = 156 (s = senior ticket price; c = child ticket price)

2nd concert: 3s + 2c = 88

Easiest to eliminate the "s" terms by multiplying 2nd eqn by -2

6s + 3c = 156

-6s - 4c = -176 and add.

-c = -20 so the child tickets are $20.

Substituting into the 1st eqn: 6s + 3(20) = 156

6s = 156 - 60 = 96

s = $16 (Why are the kids tickets more expensive???)

Answer 2

Hi Angus, Lets try and write these equations.

we have 2 variables here. the price of senior tickets, lets call this x... and the price of child tickets.. lets call that y.

now we know we have sold 6 seniors and 3 childs tickets totaling $156.

156= 6x + 3y

next we also made $88 by selling 3 senior and 2 childs

88= 3x + 2y.

we have 2 equations now.

156= 6x + 3y & 88= 3x + 2y.

how do we solve for x and y? well thats simple. take your favorite equation and isolate one variable. so here is what i would do:

88=3x+2y ; subtract 2y

88-2y=3x ; now divide by 3

(88-2y)/3= x

so put that into the first equation but replace 'x' and solve for y/

156= 6((88-2y)/3) + 3y ; you can eliminate the denominator by divind 6 by 3

156 = 2(88-2y) + 3y; multiply by 2

156 = 176-4y+3y; combine 'y's

156=176-y

-20= -y

y=20

we know each child ticket is $20. so now take that into one of the equations and solve for x!

88= 3x + 2y

88=3x+2(20)

88=3x+40

48=3x

x=16

DONE!!

Senior tickets are $16 and child tickets are $20!!

hope this helps.

-R

Answer 3

First define your variables. Let's let "s" represent the price of a senior citizen ticket and let "c" represent the price of a child ticket.

So if the school sold 6 senior citizen tickets and 3 child ticket for a total of $156 you could say

6s + 3c = 156

You could simplify this equation by dividing both sides by 3 to get:

2s + c = 52 meaning c = 52 - 2s

And if they sold 3 senior citizen tickets and 2 child tickets for $88 then:

3s + 2c = 88

Now, plug into this equation "52 - 2s" wherever you see "c" because c = 52 - 2s

3s + 2(52 - 2s) = 88

3s + 104 - 4s = 88

-s + 104 = 88

-s = 88 - 104

-s = -16

s = 16

Then, because c = 52 - 2s:

c = 52 -2(16)

c = 52 - 32

c = 20

So senior citizen tickets are $16 and child tickets are $20

Answer 4

Your 2nd sentence can be symbolized as 6S + 3C = 156, and the 3rd sentence as 3S + 2C = 88.