# Algebra

On the opening night of a play at a local theatre, 895 tickets were sold for a total of \$10,514. Adult tickets cost \$14 each, children's tickets cost \$11 each and senior citizen tickets cost \$8 each. If the combined number of children and adult tickets exceeded twice the number of senior citizen tickets by 295, than how many tickets of each type were sold?

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children -- y
seniors --- z

x+y+z = 895 , #1

14x +11y + 8z = 10514 , #2

translation of:
"If the combined number of children and adult tickets exceeded twice the number of senior citizen tickets by 295"
---> x+y > 2z by 295
x+y = 2z + 295
x + y - 2z = 295 #3

#1 - #3:
3z = 600
z = 200
so #1
---> x+y + 200 = 895
y= 695 - x

sub into #2:
14x + 11(695-x) +8(200) = 10514
14x + 7645 - 11x + 1600 = 10514
3x = 1269
x = 423
then y = 695 - 423 = 272

So they sold
272 children and
200 senior tickets

checK
14(423) + 11(272) + 8(200) = 10514, YEAHHH

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2. Ticket Sales. Stacey is selling tickets to the school play. The tickets are \$7 for adults and \$4 for children. She sells twice as many adult tickets as children's tickets and brings in a total of \$306. How many of each kind of ticket did she sell?

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