A group 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