Adult tickets to a play cost $22. Tickets 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
A is correct
anyone got all the answers?
Well, it seems like we have a clowning math problem here! Let's use some equations to find out the answer.
Let's call the number of children in the group "C" and the number of adults "A". We have two equations:
1) A + C = 11 (because the total number of people in the group is 11)
2) 22A + 15C = 228 (because the total cost of the tickets is $228)
Now let's solve this funny system of equations!
From equation 1, we can isolate A to get A = 11 - C.
Now we can substitute A in equation 2 with this expression:
22(11 - C) + 15C = 228
Let's get rid of those parentheses:
242 - 22C + 15C = 228
Combine like terms:
-7C = -14
Time to divide both sides by -7:
C = 2
And now, let's substitute this value of C into equation 1 to find A:
A + 2 = 11
A = 9
So, the number of children (C) is 2 and the number of adults (A) is 9.
Looks like option A. 2 children, 9 adults is the correct answer! Now, go enjoy the play and laugh your socks off!
Let's assume that the number of adults in the group is represented by 'a', and the number of children is represented by 'c'.
From the given information, we can form the following system of equations:
Equation 1: a + c = 11 (since the total number of people in the group is 11)
Equation 2: 22a + 15c = 228 (since the total cost of the tickets for the group is $228)
To solve this system of equations, we can use the method of substitution.
From Equation 1, we can rewrite it as c = 11 - a.
Substituting this value of c into Equation 2, we get:
22a + 15(11 - a) = 228
Expanding and simplifying, we have:
22a + 165 - 15a = 228
Combining like terms, we get:
7a + 165 = 228
Subtracting 165 from both sides of the equation, we have:
7a = 63
Dividing both sides of the equation by 7, we get:
a = 9
Substituting this value of a into Equation 1, we find:
9 + c = 11
Solving for c, we get:
c = 11 - 9
c = 2
Therefore, there were 9 adults and 2 children in the group.
The correct answer is A. 2 children, 9 adults.
To solve this problem, we can write a system of equations based on the given information.
Let's assume the number of adult tickets sold is "a" and the number of child tickets sold is "c".
From the given information, we know that:
1) Adult tickets cost $22 each and child tickets cost $15 each.
Therefore, the total cost of adult tickets is 22a and the total cost of child tickets is 15c.
2) The total cost of the tickets for the group of 11 people is $228.
Therefore, the total cost of all the tickets (adult + child) is 228.
We can now write the system of equations:
Equation 1: 22a + 15c = 228 (total cost of all tickets)
Equation 2: a + c = 11 (total number of people in the group)
To solve this system, we can use the method of substitution or elimination.
Method of Substitution:
Step 1: Solve Equation 2 for "a" in terms of "c".
a = 11 - c
Step 2: Substitute the value of "a" from Step 1 into Equation 1.
22(11 - c) + 15c = 228
Step 3: Simplify and solve for "c".
242 - 22c + 15c = 228
-7c = 228 - 242
-7c = -14
c = -14 / -7
c = 2
Step 4: Substitute the value of "c" into Equation 2 to find "a".
a + 2 = 11
a = 11 - 2
a = 9
Therefore, the number of children and adults in the group is 2 children and 9 adults. So, the correct answer is A.