Two families bought tickets for a game. one family paid $71 for 6 adults and 2 children. another family paid $56.50 for 4 children and 3 adults. how much do the tickets cost.

Adult Ticket cost $9.50 and Children Ticket cost $7.00

Step-by-step explanation:

Let single adult tickets cost "a" and single children ticket cost "c"

6 adult and 2 children ticket is $71, we can write:

6a + 2c = 71

Also,

3 adult and 4 children tickets cost $56.50, so we can write:

3a + 4c = 56.5

We multiply 2nd equation by "-2", to get:

-2 * (3a + 4c = 56.5) = -6a -8c = -113

Now we add this equation with 1st and eliminate a and solve for c:

6a + 2c = 71

-6a -8c = -113

-6c = -42

c = -42/-6

c = 7

To find a, we can plug this into 1st equation and then get our answer.

6a + 2c = 71

6a + 2(7) = 71

6a + 14 = 71

6a = 57

a = 57/6

a = 9.5

Hence,

Adult Ticket cost $9.50 and Children Ticket cost $7.00