adults --- x
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
423 adult
272 children and
200 senior tickets
checK
14(423) + 11(272) + 8(200) = 10514, YEAHHH
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?
2 answers
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