SOLUTION: Tickets for a play at the community theater cost $16 for an adult and $2 for a child. If 210 tickets were sold and the total receipts were $2380, how many of each type of ticket we
Algebra ->
Customizable Word Problem Solvers
-> Mixtures
-> SOLUTION: Tickets for a play at the community theater cost $16 for an adult and $2 for a child. If 210 tickets were sold and the total receipts were $2380, how many of each type of ticket we
Log On
Question 78043: Tickets for a play at the community theater cost $16 for an adult and $2 for a child. If 210 tickets were sold and the total receipts were $2380, how many of each type of ticket were sold? Answer by tutorcecilia(2152) (Show Source):
You can put this solution on YOUR website! Let Adult tickets = A
Let Children's tickets = C
Than, Adult + Children=210
or A+C=210
.
$16(Adult)+$2(Children)=$2380
or 16a+2C=2380
.
Solve the system of equations using any method: addition, subtraction or substitution:
A+C=210
16A+2C=2380
.
I will use addition/subtraction:
(-16)A+C=210 [multiply by (-16) in order to eliminate the x-terms]
16A+2C=2380
.
-16A-16C=-3360
+16A+2C=+2380
_________________
0A-14C=-980
.
-14C=-980 [solve for the C-term]
C=70
C=Children's tickets = $70
.
Plug C=70 back into either of the original equations and solve for the cost of the Adult (A) tickets:
A+C=210
70+A=210
A=210-70
140
Checking 140+70=210 [checks out]
.
or
.
$16(Adult)+$2(Children)=$2380
(16)(140)+(2)(70)=2380
2380=2380 [also checks out]
