Question 623771
I understand the concept but cannot arrive at the correct answers I think I am messing up the last equation. I keep getting the number of adult tickets is 74 but I know that is not right.  A movie theater charges $7 for adults, $5 for children, and $4 for seniors over age 60. The theater sold 222 tickets and took in $1383. If twice as many adult tickets were sold as the total of children and senior tickets, how many tickets of each kind were sold.


Let amount of adults', children's, and seniors' tickets sold be A, C, and S, respectively


Then:
A + C + S = 222 ---------- eq (i)
7A + 5C + 4S = 1,383 ---- eq (ii)
A = 2(C + S) ---- A = 2C + 2S


2C + 2S + C + S = 222 ----- Substituting 2C + 2S for A in eq (i)
3C + 3S = 222
3(C + S) = 3(74)
C + S = 74 ------ eq (iii)


7(2C + 2S) + 5C + 4S = 1,383 ----- Substituting 2C + 2S for A in eq (ii)
14C + 14S + 5C + 4S = 1,383
19C + 18S = 1,383 ---- eq (iv)


C + S = 74 ------ eq (iii)
19C + 18S = 1,383 ---- eq (iv) 
- 18C – 18S = - 1,332 ------- Multiplying eq (iii) by – 18 ---- eq (v)
C = 1,383 – 1,332 ------ Adding eqs (iv) and (v)


C, or amount of children’s tickets sold = {{{highlight_green(51)}}}


51 + S = 74 ----- Substituting 51 for C in eq (iii)
S = 74 – 51


S, or amount of seniors’ tickets sold = {{{highlight_green(23)}}}


Since A = 2C + 2S, then A = 2(51) + 2(23) ----- A = 102 + 46 


A, or amount of adults’ tickets sold = {{{highlight_green(148)}}}


I'm sure you can do the check.


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