Agroup of children and their parents went to the skating rink. there were a total of 30 people in the group, the cost for each adult was $12 and the cost for each child was $8. the total amount paid was $280. let a represent the number of adults and c represent the number of children.

C=number of children
a=number of adults
total number os 30 so 
a+s=30

cost for all adult=12a
cost for all child=8c
total cost=12a+8c
280=12a+8c
divide by 4 to make it easier
70=3a+2c

so we have
a+c=30
3a+2c=70
multiply firse equation by -2 and add to second equaiton

-2a-2c=-60
3a+2c=70 +
1a+0c=10

a=10
subsitute
a+c=30
10+c=30
c=20

20 childeren
10 adults