I need help finding the number of children who attended a movie premier

Question

Six hundred people attended the premiere of a motion picture. Adult tickets cost $9, and children were admitted for $6. If box office receipts totaled $4260, how many children attended the premiere?

Answer 1

Let A = number of adult tickets, and C = number of child tickets

Then A + C = 600 tickets; A = 600 - C

Then $9 x A + $6 x C = $4260

Then $9 (600 - C) + $6C = $4260, which becomes $5400 - $9C + $6C = $4260

Combining, we get $5400 - $9C + $6C = $4260

Rearranging, we get $5400 - $4260 = $3C

Then, $1140 = $3C, which becomes 380 = C

Then, the number of adult tickets is 600 - 380 = 220

Proof: 220 tickets x $9/Adult + 380 tickets x $3/child = $4260