Write two equations to represent the total amount raised from the dinner and the total.?

Question

At the high school band's annual spaghetti dinner, the members served 210 dinners and collected $935. The band leader did not designate which ticket was an adult or child dinner. You need to know that to prepare the correct amount of food and for future planning. Each adult dinner cost $6 and each child's dinner cost $3.50.

Let a = number of adult dinners
Let c = number of child dinners

Answer 1

a+c = 210, and so c = 210 - a. So we have:
935 = 6a + 3.5(210 - a), or 2.5a + 735 = 935, and 2.5a = 200, so a = 80, and c = 130

Answer 2

a + c = 210

6a + 3.5c = 935

multiply the first by 7 and the second by 2

7a + 7c = 1470

12a + 7c = 1870

so
5a = 400
a = 80
c = 130