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22 May 2020, 10:21
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A
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Difficulty:
35%
(medium)
Question Stats:
79% (02:53) correct
21%
(03:07)
wrong
based on 666
sessions
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A theater with 600 seats sells tickets at $1.20, $1.80, or $2.40 per seat. On Wednesday evening, 1/3 of the tickets sold were at $1.80 per seat and the total receipts from the sale of 600 tickets was $1,020. How many of the tickets sold were at $2.40 per seat?
A. 150
B. 160
C. 200
D. 250
E. 300
PS20373
A. 150
B. 160
C. 200
D. 250
E. 300
PS20373
22 May 2020, 10:33
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Bunuel
A theater with 600 seats sells tickets at $1.20, $1.80, or $2.40 per seat. On Wednesday evening, 1/3 of the tickets sold were at $1.80 per seat and the total receipts from the sale of 600 tickets was $1,020. How many of the tickets sold were at $2.40 per seat?
A. 150
B. 160
C. 200
D. 250
E. 300
PS20373
A. 150
B. 160
C. 200
D. 250
E. 300
PS20373
Given: 600 tickets were sold
One third of those tickets were at $1.80 per seat
1/3 of 600 = 200
So, 200 tickets sold for $1.80 per seat
And the remaining 400 tickets were sold for either $1.20 each of $2.40 each
Let x = the NUMBER of tickets sold for $2.40
So, 400 - x = the NUMBER of tickets sold for $1.20
The total receipts from the sale of 600 tickets was $1,020
In other words: (receipts from the $1.20 tickets) + (receipts from the $1.80 tickets) + (receipts from the $2.40 tickets) = $1,020
(200)($1.80) = $360
So, $360 = the total receipts from the $1.80 tickets
Likewise, (400 - x)($1.20) = the total receipts from the $1.20 tickets
And (x)($2.40) = the total receipts from the $2.40 tickets
Substitute values into our "word equation" to get: (400 - x)($1.20) + $360 + (x)($2.40) = $1020
Expand to get: 480 - 1.20x + 360 + 2.40x = 1020
Simplify to get: 840 + 1.20x = 1020
Subtract 840 from both sides: 1.20x = 180
Solve: x = 180/1.20 = 150
Answer: A
Cheers,
Brent
General Discussion
24 May 2020, 03:02
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A.
Total Tickets at $1.80 = 1/3 * 600 = 200
Total cost for 200 tickets at $1.80 = $360
Remaining count of tickets sold at $1.20 & $2.40 = 400
Let total count of tickets sold at $1.20= x
total count of tickets sold at $2.40= 400-x
Total cost for tickets sold at $1.20 = 1.20x
Total cost for tickets sold at $2.40 = 2.40(400-x)
As per question: 1.20x + 360 + 2.40 (400-x) = 1020
Solving for x, x = 250
Tickets at $2.40 = 400-250 = 150
Total Tickets at $1.80 = 1/3 * 600 = 200
Total cost for 200 tickets at $1.80 = $360
Remaining count of tickets sold at $1.20 & $2.40 = 400
Let total count of tickets sold at $1.20= x
total count of tickets sold at $2.40= 400-x
Total cost for tickets sold at $1.20 = 1.20x
Total cost for tickets sold at $2.40 = 2.40(400-x)
As per question: 1.20x + 360 + 2.40 (400-x) = 1020
Solving for x, x = 250
Tickets at $2.40 = 400-250 = 150
