adult tickets to a play cost $22. tichets for children cost $15. tickets for a group of 11 people cost a total of $228. write and solve a system of equations to find how many children and how many adults were in the group.
a ) 2 children, 9 adults
b ) 4 children , 7 adults
c ) 5 children, 6 adults
d ) 7 children, 4 adults
Let x represent the number of adult tickets sold and y represent the number of children tickets sold.
From the given information, we have the following two equations:
1) x + y = 11 (equation 1) - representing the total number of people in the group.
2) 22x + 15y = 228 (equation 2) - representing the total cost of the tickets for the group.
To solve the system of equations, we can use either the substitution or elimination method.
Using the substitution method, we can solve equation 1 for x:
x = 11 - y
Substituting this value of x in equation 2, we have:
22(11 - y) + 15y = 228
242 - 22y + 15y = 228
-7y = -14
y = 2
Substituting the value of y back into equation 1, we have:
x + 2 = 11
x = 9
Therefore, there were 9 adults and 2 children in the group.
The correct answer is:
a) 2 children, 9 adults