Question 1056090
On the opening night of a play at a local​ theater, 992 tickets were sold for a total of  ​$11,680. Adult tickets cost ​$14 each.​ Children's tickets cost ​$11 ​each, and senior citizen tickets cost ​$8 each. If the combined number of children and adult tickets exceeded twice the number of senior citizen tickets by 287​, then how many tickets of each type were​ sold?
<pre>Let number of adult, children, and senior citizen tickets sold, be A, C, and S, respectively
Then we get: A + C + S = 992 -------- eq (i)
Also, 14A + 11C + 8S = 11,680 ------- eq (ii)
And, A + C - 2S = 287 ------- eq (iii)
3S = 705 ------ Subtracting eq (iii) from eq (i) 
S, or {{{705/3}}}, or {{{highlight_green(matrix(1,6, 235, senior, "citizens'", tickets, were, sold))}}}

A + C + 235 = 992 _----- Substituting 235 for S in eq (i)
A + C = 992 - 235_____A + C = 757_____A = 757 - C ----- eq (iv)
14(757 - C) + 11C + 8(235) = 11,680 ---- Substituting 757 - C for A, and 235 for S in eq (ii)
10,598 - 14C + 11C + 1,880 = 11,680
- 14C + 11C + 12,478 = 11,680 
- 3C = 11,680 - 12,478	
- 3C = - 798	
C, or {{{(- 798)/(- 3)}}}, or {{{highlight_green(matrix(1,5, 266, "children's", tickets, were, sold))}}}

A = 757 - 266 ------ Substituting 266 for C in eq (iv)	
A, or {{{highlight_green(matrix(1,5, 491, "adults'", tickets, were, sold))}}}