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So since there are a total of 20 purchased tickets, the first equation should be

a + c = 20

Since it's a total of 30$ the second equation should be

3a + 1c = 30

In the first equation you isolate either a or c. We'll isolate a by moving c to the other side. The equation should now be a = 20 - c. Now that we know what a equals, we plug it in to the second equation 3(20 - c) + c = 30. Simplify 60 - 2c = 30 move 2c to the other side. 60= 30 + 2c. Subtract 30 on both sides . 30= 2 c. Divide by 2. 15 = c

Now we know that c=15 we plug that in the first equation to solve for a

a + 15 = 20 . subtract 15 from both sides to get a = 5.

Now we know that C = 15 and A = 5. This means that. Ms Ramirez purchased 15 tickets for children and 5 tickets for adults