Find the price of one senior citizen ticket and one student ticket

Question

The school that Kristen goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 8 senior citizen tickets and 7 student tickets for a total of $146. The school took in $80 on the second day by selling 4 senior citizen tickets and 4 student tickets. What is the price each of one senior citizen ticket and one student ticket?

Answer 1

8c + 7s = 146

4c +4s = 80

8c +8s = 160

s = $14 for student

c +s = 20

c = 20-14 = $6 for senior citizen

Answer 2

x = price of senior ticket

y = price of student ticket

create two equations representing amount of sales for tickets on two days

8x + 7y = 146

4x + 4y = 80

multiply second equation by 2 and subtract from 1st equation:

8x + 7y = 146

-(8x + 8y = 160)

-y = -14

y = 14

substitute 14 for y in 2nd equation and solve for x:

4x + 4(14) = 80

4x = 24

x = 6

$6 for senior tickets

$14 for student tickets

Answer 3

1) First, you need to begin by creating your two separate equations. For the purpose of my explanation, senior citizen tickets are represented as (x) and student tickets as (y).

8x + 7y = $146

4x + 4y = $80

2) Next, you need to make the coefficient of either x or y the same in both equations. Looking at them, it would be easier to make the x coefficients the same by multiplying the second equation by 2. This is so that you can later subtract the equations and get a 0 for either x or y, thereby leaving only one variable.

2* (4x + 4y = 80)

=8x + 8y = 160

3) Now subtract the second equation from the first equation.

8x + 7y = 146

-(8x + 8y = 160)

4) Solve

-y = - 14

y= 14

5) Plug in y to either equation to find x.

4x + 4(14) = 80

4x + 56 = 80

4x = 24

x = 6