use systems of equations to solve the application problem. BE sure to show the system used.?

Question

Ticket prices:
Tickets for the show cost $2.00 for adults and $ 1.50 for children. How many adult tickets and how many children 's tickets were sold if a total of 127 tickets were sold for $214? :)

Answer 1

Adult ticket = x (price = $2.00 / ticket)
Children ticket = y (price = $1.50 / ticket)

x + y = 127 --- (1)
2x + 1.5y = 214 --(2)
2x(1)
2x + 2y = 254 ---(3)
(3)-(2)
0.5y = 40
y = 80
x = 127 - 80 = 47

Adult ticket sold = 47
Children ticket sold = 80

Answer 2

c for # of children tickets
a for # of adult tickets

cost equation would be:
2a + 1.5c = 214

quantity equation would be:
a + c = 127

now you have your system and you have to solve. one method would be the elimination method (aka addition method or linear combination method). To do this, you must multiply the quantity equations by -2 to eliminate the a-variable so you can solve for c.

2a + 1.5c = 214
-2a + -2c = -254

-.5c = -40
c = 80

now if 80 children tickets were sold, you can figure out # of adult tickets:
a + 80 = 127
a = 47

now check:
2(47) + 1.5(80) = 94 + 120 = 214 true

so 47 adult tickets and 80 children tickets

Answer 3

Let a be number of adults and b be the number of children

"total of 127 tickets"
This tells you that the sum of adults and chidren is 127 so:
a+b=127

"sold for $214"
This tells total cost. Since adults payed 2 and children payed 1.5, adults would of payed 2a, children would have payed1.5b. these two should add up to 214:
2a+1.5b = 214

giving you two equations
a+b=127
2a+1.5b = 214

multiply the top by 4 and the bottom by 2 you can subtract and eliminate a

4a+4b=508
4a+3b=428
---------------------
0a + b = 80

b=80
a+b=127
a=80 = 127
a=47

checking
80+47 = 127
127=127

2(47) + 80(1.5) = 214
214=214

47 adults and 80 children

Answer 4

Let the no. of children tickets sold be x.kTherefore,the no. of adults tickets sold is 127-x
By the problem,
1.5x+(127-x)*2=$214
=> 1.5x+254-2x=214
=>-0.5x=-40
=>x=80
Therefore 80 children tickets were sold