SOLUTION: 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 tot

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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?
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

On the first day of ticket sales the school sold 9 senior tickets price $x per ticket
and 14 child tickets price $y per ticket for a total of $227.
9x+14y =227---------(1)

The school took in $171 on the second day by selling 3 senior tickets and 12 child ticket at the same price
3x+12y = 171
9.00 x + 14.00 y = 227.00


3.00 x + 12.00 y = 171.00 .............2
Eliminate y
multiply (1)by -6.00
Multiply (2) by 7.00
-54.00 x -84.00 y = -1362.00
21.00 x 84.00 y = 1197.00
Add the two equations
-33.00 x = -165.00
/ -33.00
x = 5.00
plug value of x in (1)
9.00 x + 14.00 y = 227.00
45.00 + 14.00 y = 227.00
14.00 y = 182.00
y = 13.00
Ans x = 5.00
y = 13.00




Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

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?
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 

Now, just substitute 13 for C in eq (ii) and you should be able to find the cost of a senior's ticket. 

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