Let the number of adult be x and the number of children be y.
There is a total of 11 people
x + y = 11
Total cost of tickets is $228
22x + 15y = 228
x + y = 11 ----------------- (1)
22x + 15y = 228 ---------(2)
From (1):
x+ y = 11
x = 11 - y --- sub into (2)
22 (11 - y) + 15y = 228
242 - 22y + 15y = 228
-7y = 228 - 242
-7y = -14
y = 2 ---- sub into (1)
x+ 2 = 11
x = 9
Number of adult tickets = 9
Number of child tickets = 2
Answer: Late 200 tho
Step-by-step explanation:
For this case we must solve a system of two equations with two unknowns, given by "x" and "y".
We have:
![y = 4x + 11\ (1)\\y = -2x-1\ (2)](https://tex.z-dn.net/?f=y%20%3D%204x%20%2B%2011%5C%20%281%29%5C%5Cy%20%3D%20-2x-1%5C%20%282%29)
We multiply (2) by -1:
![-y = 2x + 1\ (3)](https://tex.z-dn.net/?f=-y%20%3D%202x%20%2B%201%5C%20%283%29)
We add (1) and (3):
![y-y = 4x + 2x + 11 + 1\\0 = 6x + 12](https://tex.z-dn.net/?f=y-y%20%3D%204x%20%2B%202x%20%2B%2011%20%2B%201%5C%5C0%20%3D%206x%20%2B%2012)
Clearing x:
![-12 = 6x\\x = \frac {-12} {6}\\x = -2](https://tex.z-dn.net/?f=-12%20%3D%206x%5C%5Cx%20%3D%20%5Cfrac%20%7B-12%7D%20%7B6%7D%5C%5Cx%20%3D%20-2)
We substitute
in (2)
![y = -2 (-2) -1\\y = 4-1\\y = 3](https://tex.z-dn.net/?f=y%20%3D%20-2%20%28-2%29%20-1%5C%5Cy%20%3D%204-1%5C%5Cy%20%3D%203)
Thus, the solution of the system is ![(x, y) = (- 2,3)](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%3D%20%28-%202%2C3%29)
Answer:
The solution of the system is ![(x, y) = (- 2,3)](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%3D%20%28-%202%2C3%29)