SOLUTION: Amy's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 10 senior citizen tickets and 1 student ticket for a total of $54. The school to

Algebra ->  Systems-of-equations -> SOLUTION: Amy's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 10 senior citizen tickets and 1 student ticket for a total of $54. The school to      Log On


   

Question 1109593: Amy's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 10 senior citizen tickets and 1 student ticket for a total of $54. The school took in $74 on the second day by selling 1 senior citizen ticket and 5 student tickets. Find the price of a senior citizen ticket and the price of a student ticket
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x=senior and y=student
10x+y=54
x+5y=74
-10x-50y=-740
-49y=-686
y=$14 student
x=$4 senior

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the price of a senior ticket
Let +b+ = the price of a student ticket
-------------------------------------------
(1) +10a+%2B1%2Ab+=+54+
(2) +1%2Aa+%2B+5b+=+74+
--------------------------
Multiply both sides of (1) by +5+
and subtract (2) from (1)
(1) +50a+%2B+5b+=+270+
(2) +-a+-+5b+=+-74+
----------------------------
+49a+=+196+
+a+=+4+
and
(1) +10%2A4+%2B+b+=+54+
(1) +40+%2B+b+=+54+
(1) +b+=+14+
----------------------------
A senior ticket costs $4
A student ticket costs $14
----------------------------
check:
(2) +a+%2B+5b+=+74+
(2) +4+%2B+5%2A14+=+74+
(2) +4+%2B+70+=+74+
(2) +74+=+74+
OK