SOLUTION: A theatre has a seating capacity of 900 and charges 4$ for children, 6$ for students and 8$ for adults. At a certain screening with full attendance, there were half as many adults
Question 1000083: A theatre has a seating capacity of 900 and charges 4$ for children, 6$ for students and 8$ for adults. At a certain screening with full attendance, there were half as many adults as students and children combined. The receipts total 5600$. How many children attended the show? Answer by ankor@dixie-net.com(22740) (Show Source):
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let a no. of adults
let c = no. of children
let s = no. of students
:
write an equation for each statement
:
A theatre has a seating capacity of 900
a + c + s = 900
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At a certain screening with full attendance, there were half as many adults as students and children combined.
a = (c + s)
multiply both sides by 2
2a = c + s
2a - c - s = 0
:
The receipts total 5600$.(charges 4$ for children, 6$ for students and 8$ for adults.)
8a + 4c + 6s = 5600
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Use elimination here,
a + c + s = 900
2a - c - s = 0
----------------------Adding eliminates c and s, find a
3a = 900
a = 900/3
a = 300 adults
:
using the first equation
300 + c + s = 900
c + s = 900 - 300
c + s = 600
s = (600-c)
:
Replace a with 300 and s with (600-c) in the 3rd eq
8(300) + 4c + 6(600-c) = 5600
2400 + 4c + 3600 - 6c = 5600
4c - 6c + 6000 = 5600
-2c = 5600 - 6000
-2c = -400
c = -400/-2
c = 200 children attended the show?
