SOLUTION: 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 ti

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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?

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
x child tickets
y adult tickets
z senior tickets



You might want to try to first eliminate z, simplify the system to linear equations in x and y; and continue onward to finish. Alternatively, you could use other standard matrix row reductions or choose substitution method.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
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?
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 , or 



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 , or 



A = 757 - 266 ------ Substituting 266 for C in eq (iv)	

A, or  

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