Respuesta :
Answer:
The answer to your question is There were sold 166 adult tickets and 294
children tickets.
Step-by-step explanation:
Data
Total number of seats = 460
cost for adults = a = $52
cost for children = c = $26
Total cost = $16276
Process
1.- Write equations to solve this problem
a + c = 460 Equation l
52a + 26c = 16276 Equation ll
2.- Solve the system of equation by substitution.
-Solve equation l for a
a = 460 - c
-Substitute a in equation ll
52(460 - c) + 26c = 16276
-Expand
23920 - 52c + 26c = 16276
-Simplify
-26c = 16276 - 23920
-26c = -7644
c= -7644/-26
c = 294
3.- Find a
a = 460 - 294
a = 166
Answer: 166 adult tickets and 294 children tickets were sold.
Step-by-step explanation:
Let x represent the number of adult tickets that were sold.
Let y represent the number of children tickets that were sold.
The ticket prices for a recent play were $52 for adults and $26 for children. If the total proceeds were $16,276 for a sold-out matinee, it means that
52x + 26y = 16276- - - - - - - - - 1
The theater contains 460 seats. Since it was a sold-out matinee, it means that
x + y = 460
Substituting x = 460 - y into equation 1, it becomes
52(460 - y) + 26y = 16276
23920 - 52y + 26y = 16276
- 52y + 26y = 16276 - 23920
- 26y = - 7644
y = - 7644/- 26
y = 294
x = 460 - y = 460 - 294
x = 166
