Please help, I need an explanation!

A circus charges $5 per child ticket and $8 per adult ticket. There were 136 tickets sold for a total of $830. How many child tickets and how many adult tickets were purchased?

I know that I need to use c + a =136 and 5c + 8a = 830

50 adult

86 child

Step-by-step explanation:

c + a =136

5c + 8a = 830

These are the two equations to use

c is the number of child tickets and a is the number of adult tickets

The total number of tickets is 136

The child tickets are 5 dollars apiece and the adult tickets are 8 dollars apiece and the total amount made is 830

I will use elimination

Multiply the first equation by -5

-5(c+a) = -5*136

-5c-5a =-680

Then add this to the second equation

-5c-5a =-680

5c +8a = 830

    3a  = 150

Divide each side by 3

3a/3 = 150/3

a = 50

Now we can find c

a+c = 136

50 + c = 136

Subtract 50 from each side

50+c-50 =136-50

c = 86

child tickets: 86

adult tickets: 50

Step-by-step explanation:

C + A = 136

C = 136 - A

5C + 8A = 830

5(136 - A) + 8A = 830

680 - 5A + 8A = 830

3A = 150

A = 50

C = 136 - 50

C = 86

answer: the common difference is -0.10