SOLUTION: A theater has a seating capacity of 720 and charges $2 for children (x), $4 for students (y), and $6 for adults (z). At a certain screening with full attendance, there were half as
Algebra.Com
Question 404777: A theater has a seating capacity of 720 and charges $2 for children (x), $4 for students (y), and $6 for adults (z). At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $3080. How many children attended the show?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A theater has a seating capacity of 720 and charges $2 for children (x), $4 for students (y), and $6 for adults (z).
At a certain screening with full attendance, there were half as many adults as children and students combined.
The receipts totaled $3080.
How many children attended the show?
--------------------------
Equations:
People: x + y + z = 720
Quantity: z = (1/2)(x+y)
Values: 2x + 4y + 6z = 3080
===================================
Rearrange:
x + y + z = 720
x + y -2z = 0
x +2y +3z = 1540
----------------------
Use whatever method you know to get:
x = 140
y = 340
z = 240
========================
Cheers,
Stan H.
========================
RELATED QUESTIONS
A theater has a seating capacity of 600 and charges $3 for children, $5 for students, and (answered by solver91311)
Formulate a system of equations for the situation below and solve.
A theater has a... (answered by math_tutor2020,josgarithmetic,ikleyn,MathTherapy,greenestamps)
Formulate a system of equations for the situation below and solve.
A theater has a... (answered by ankor@dixie-net.com)
Formulate a system of equations for the situation below and solve.
A theater has a... (answered by josgarithmetic)
Formulate a system of equations for the situation below and solve.
A theater has a... (answered by ikleyn)
a theater has a seating capacity of 900 and charges $4 for children, $6 for students, and (answered by josmiceli)
Formulate a system of equations for the situation below and solve.
A theater has a... (answered by macston)
A theater has a seating capacity of 1050 and charges $3 for children, $5 for students,... (answered by josgarithmetic,ikleyn)
A theatre has a seating capacity of 900 and charges 4$ for children, 6$ for students and... (answered by ankor@dixie-net.com)