Question

Eduardo's school is selling tickets to the annual dance competition on the first day of ticket sales the school sold 11 senior citizen tickets and 2 studentickets for a total of 172. The school look in $198 on the second day by selling 9 senior citizen tickets and 8 student tickets Find the price of a senior citizen ticket and the price of a student ticket.​

Answer 1

The price of a senior citizen ticket is approximately $11.23 and the price of a student ticket is approximately $24.24.

Step-by-step explanation:

Let's denote the price of a senior citizen ticket as x and the price of a student ticket as y.

From the given information, we can form two equations:

11x + 2y = 172 (Equation 1)

9x + 8y = 198 (Equation 2)

We can solve this system of equations by elimination or substitution. Let's solve it by elimination:

Multiplying Equation 1 by 4 and Equation 2 by 2, we have:

44x + 8y = 688 (Equation 3)

18x + 16y = 396 (Equation 4)

Now, subtracting Equation 4 from Equation 3, we get:

26x = 292

Dividing both sides by 26, we find:

x = 11.23

Substituting the value of x into Equation 1, we can solve for y:

11(11.23) + 2y = 172

123.53 + 2y = 172

Subtracting 123.53 from both sides, we get:

2y = 48.47

Dividing both sides by 2, we find:

y ≈ 24.24

Therefore, the price of a senior citizen ticket is approximately $11.23 and the price of a student ticket is approximately $24.24.