Help? The school john goes to is selling tickets to the annual dance competition . On the first day of sales the school sold 2 senior citizen tickets and 13 student tickets for a total of $108. The school took in$144 on the second day selling 4 senior tickets and 14 student tickets. Find the price of a student and senior ticket.

2S + 13s = 108

4S + 14s = 144

Multiply top equation by 2 and subtract the second from that product to find s. Insert that s value into either equation to find S.

To find the price of a student and senior ticket, we can set up a system of linear equations based on the given information.

Let's assume the price of a student ticket is 's', and the price of a senior citizen ticket is 'c'.

On the first day, the school sold 2 senior tickets and 13 student tickets for a total of $108. We can express this information as the equation:

2c + 13s = 108 ...........(1)

On the second day, the school sold 4 senior tickets and 14 student tickets for a total of $144. We can express this information as the equation:

4c + 14s = 144 ...........(2)

Now, we can solve this system of equations using any method such as substitution, elimination, or matrix.

Let's solve it using the elimination method:

Multiplying equation (1) by 4 and equation (2) by 2, we get:

8c + 52s = 432 ............(3)
8c + 28s = 288 ............(4)

Subtracting equation (4) from equation (3):

(8c + 52s) - (8c + 28s) = 432 - 288
24s = 144
s = 144/24
s = 6

Now, substituting the value of 's' back into equation (1):

2c + 13(6) = 108
2c + 78 = 108
2c = 108 - 78
2c = 30
c = 30/2
c = 15

Therefore, the price of a student ticket is $6, and the price of a senior ticket is $15.

To find the price of a student and senior ticket, we can set up a system of equations based on the given information. Let's denote the price of a student ticket as "S" and the price of a senior ticket as "C".

From the first day of sales, we know that:
2C + 13S = 108 (Equation 1)

And from the second day of sales, we know that:
4C + 14S = 144 (Equation 2)

Now we can solve this system of equations by either substitution or elimination.

Let's use the elimination method to eliminate the variable "C".
Multiply Equation 1 by 2 and Equation 2 by -1 to eliminate the coefficient of "C":
(2C + 13S) * 2 = 108 * 2 ---> 4C + 26S = 216 (Equation 3)
(-4C - 14S) * -1 = 144 * -1 ---> 4C + 14S = -144 (Equation 4)

Now we can add Equation 3 and Equation 4 to eliminate "C":
(4C + 26S) + (4C + 14S) = 216 + (-144)
8C + 40S = 72 (Equation 5)

Next, we can solve Equation 5 for "S":
8C + 40S = 72
40S = 72 - 8C
S = (72 - 8C) / 40 (Equation 6)

Now we substitute Equation 6 into Equation 1:
2C + 13S = 108
2C + 13((72 - 8C) / 40) = 108

Simplify and solve for "C":
2C + (13/40)(72 - 8C) = 108
2C + (13/40)(72) - (13/40)(8C) = 108
2C + (13/5)(18) - (13/5)(2C) = 108
2C + (234/5) - (26/5)C = 108
(10/5)C - (26/5)C = 108 - (234/5)
- (16/5)C = (540/5) - (234/5)
-(16/5)C = 306/5
C = (306/5) * (-5/16)
C = - 153/8
C = - 19.125

Now substitute the value of "C" back into Equation 1 or Equation 2 to find the value of "S". Let's use Equation 1:
2C + 13S = 108
2(-19.125) + 13S = 108
-38.25 + 13S = 108
13S = 108 + 38.25
13S = 146.25
S = 146.25 / 13
S ≈ 11.25

So, the price of a senior ticket (C) is approximately $19.13, and the price of a student ticket (S) is approximately $11.25.