Question

Tickets to the museum cost $18 for adults and $12 for children. A group of 20 people went to the museum, and the tickets cost $324. The system of equations models this situation, where x is the number of adults and y is the number of children.

x-y=20
18x+12y=324

How many adults and how many children were in the group?

A.
8 adults and 12 children

B.
10 adults and 10 children

C.
12 adults and 8 children

D.
14 adults and 6 children

Answer 1

As far as i can see, there is something wrong with one of the equations that are given in the question. It is mentioned in the question that a total of 20 people went to the museum. That means that among those 20 people there were children as well as adults. So the equation that is mentioned in the question given below is wrong.
x - y = 20
The correct equation would be x + y = 20
The second equation given in the question is absolutely correct.
18x + 12y = 324
Diving both sides by 6 we get
3x + 2y = 54
Now let us get back to the first equation
x + y = 20
x = 20 - y
Putting the value of x in the second equation we get
3x + 2y = 54
3(20 - y) + 2y = 54
60 - 3y + 2y = 54
60 - y = 54
-y = 54 - 60
-y = -6
y = 6
Then we get that the number of children going to the museum is 6
So
The number of adults = 20 - 6
= 14
So the total number of adults going to the museum is 14 and the number of children going to the museum is 6. The correct option in the question is option "D".