Question

Tickets to the zoo cost $14 for adults and $10 for children. A group of 12 people went to the zoo, and the tickets cost $140. The system of equations models this situation, where x is the number of adults and y is the number of children.
x+y=12
14x+10y=140
How many adults and how many children were in the group?

A.
5 adults and 7 children

B.
6 adults and 6 children

C.
7 adults and 5 children

D.
8 adults and 4 children

Answer 1

 x is the number of adults and y is the number of children.
   x + y = 12
14x + 10y = 140
lets multiply the first equation by -10 and then add it to the second equation:
-10x - 10y = -120
14x + 10y = 140
-----------------------
4x + 0 = 20
x = 20/4
x = 5
then substitute in the original equation:
x + y = 12
5 + y = 12
y = 12 - 5
y = 7
therefore there were 5 adults and 7 children