Question 1052555: A theatre contains 454 seats and the ticket prices for a recent play were $55 for adults and $19 for children. If the total proceeds were $14,926 for a sold-out matinee, how many of each type of ticket were sold?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A theatre contains 454 seats and the ticket prices for a recent play were $55 for adults and $19 for children.
If the total proceeds were $14,926 for a sold-out matinee, how many of each type of ticket were sold?
:
let a = no. of adult tickets sold
let c = no. of children tickets
:
Write an equation for each statement
"A theatre contains 454 seats"
a + c = 454
c = (454 - a); we can use this form for substitution
:
"prices for a recent play were $55 for adults and $19 for children.
If the total proceeds were $14,926 for a sold-out matinee,"
55a + 19c = 14926
Replace c with (454-a)
55a + 19(454-a) = 14926
55a + 8626-19a = 14926
55a - 19a = 14926 - 8626
26a = 6300
a = 6300/36
a = 175 adults
then
c = 454 - 175
c = 279 children
:
:
:
Check this, find the amt for each
279*19 = 5301
175*55 = 9625
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total amt $14926
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