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How many senior tickets were sold?

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How many senior tickets were sold?

by yalanand » Sun Feb 01, 2009 12:21 am
The theater charges $5 for senior, $6 for student, and $7 for general admission tickets. On Tuesday night the theater sold 200 tickets and made $1300. They also sold twice as many general admission as student tickets. How many senior tickets were sold?

(A) 5
(B) 10
(C) 20
(D) 50
(E) 65
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Re: How many senior tickets were sold?

by piyush_nitt » Sun Feb 01, 2009 12:55 am
yalanand wrote:The theater charges $5 for senior, $6 for student, and $7 for general admission tickets. On Tuesday night the theater sold 200 tickets and made $1300. They also sold twice as many general admission as student tickets. How many senior tickets were sold?

(A) 5
(B) 10
(C) 20
(D) 50
(E) 65
Let x = senior
y = student
z = general admission


therefore

x + y + z = 200 (1)
5x + 6y + 7z = 1300 (2)
z = 2y (3)

substitute (3) in (2) and (1)

x + 3y = 200 (4)
5x + 20y = 1300 => x+4y = 260 (5)

subtract (5) - (4)

y = 60
z = 120

hence x = 200 -180 = 20

IMO C
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Master | Next Rank: 500 Posts
Posts: 424
Joined: Sun Dec 07, 2008 5:15 pm
Location: Sydney
Thanked: 12 times

Re: How many senior tickets were sold?

by piyush_nitt » Sun Feb 01, 2009 12:56 am
yalanand wrote:The theater charges $5 for senior, $6 for student, and $7 for general admission tickets. On Tuesday night the theater sold 200 tickets and made $1300. They also sold twice as many general admission as student tickets. How many senior tickets were sold?

(A) 5
(B) 10
(C) 20
(D) 50
(E) 65
Let x = senior
y = student
z = general admission


therefore

x + y + z = 200 (1)
5x + 6y + 7z = 1300 (2)
z = 2y (3)

substitute (3) in (2) and (1)

x + 3y = 200 (4)
5x + 20y = 1300 => x+4y = 260 (5)

subtract (5) - (4)

y = 60
z = 120

hence x = 200 -180 = 20

IMO C
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