1. **State the problem:** We have three types of tickets sold for a concert: adult, child, and student. We know the total tickets sold, total money collected, and the relationship between adult and child tickets. 2. **Define variables:** Let $x$ = number of adult tickets, $y$ = number of child tickets, $z$ = number of student tickets. 3. **Write equations from the problem:** - Total tickets sold: $$x + y + z = 600$$ - Total money collected: $$15x + 10y + 12z = 7816$$ - Adult tickets are twice child tickets: $$x = 2y$$ 4. **Substitute $x = 2y$ into the first two equations:** - $$2y + y + z = 600 \implies 3y + z = 600$$ - $$15(2y) + 10y + 12z = 7816 \implies 30y + 10y + 12z = 7816 \implies 40y + 12z = 7816$$ 5. **Solve the system:** From $$3y + z = 600$$, express $$z = 600 - 3y$$. Substitute into $$40y + 12z = 7816$$: $$40y + 12(600 - 3y) = 7816$$ $$40y + 7200 - 36y = 7816$$ $$4y + 7200 = 7816$$ $$4y = 616$$ $$y = 154$$ 6. **Find $z$ and $x$:** $$z = 600 - 3(154) = 600 - 462 = 138$$ $$x = 2y = 2(154) = 308$$ **Final answer:** - Adult tickets sold: $308$ - Child tickets sold: $154$ - Student tickets sold: $138$