Question 1159876

The school that Jessica goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 9 senior tickets and 14 child tickets for a total of $227. The school took in $171 on the second day by selling 3 senior tickets and 12 child tickets. What is the price of one senior ticket and one child ticket?
<pre>Let cost of a senior's and a child's ticket, be S and C, respectively
Then we get: 9S + 14C = 227 ------- eq (i)
Also, 3S + 12C = 171______3(S + 4C) = 3(57)_______S + 4C = 57_____S = 57 - 4C ------ eq (ii)
9(57 - 4C) + 14C = 227 ------ Substituting 57 - 4C for S in eq (i)
513 - 36C + 14C = 227
- 36C + 14C = 227 - 513
- 22C = - 286
Cost of a child's ticket, or {{{highlight_green(matrix(1,5, C, "=", (- 286)/(- 22), "=", "$13"))}}}
Now, just substitute 13 for C in eq (ii) and you should be able to find the cost of a senior's ticket.