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06 Aug 2026, 05:08
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A small theater sold only adult tickets and student tickets for one afternoon show. Each adult ticket cost $18, and each student ticket cost $10. If the theater sold 45 tickets for the show, how many adult tickets were sold?
(1) The average (arithmetic mean) ticket price was greater than $14.50 but less than $15.00.
(2) The total revenue from ticket sales was greater than $655 but less than $663.
(1) The average (arithmetic mean) ticket price was greater than $14.50 but less than $15.00.
(2) The total revenue from ticket sales was greater than $655 but less than $663.
06 Aug 2026, 05:08
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Official Solution:
A small theater sold only adult tickets and student tickets for one afternoon show. Each adult ticket cost $18, and each student ticket cost $10. If the theater sold 45 tickets for the show, how many adult tickets were sold?
Let \(A\) be the number of adult tickets sold. Then the number of student tickets sold was \(45 - A\).
The total revenue was:
\(18A + 10(45 - A) = 450 + 8A\)
The question asks for \(A\).
(1) The average ticket price was greater than $14.50 but less than $15.00.
Since 45 tickets were sold, the total revenue was greater than:
\(45 * 14.50 = 652.50\)
and less than:
\(45 * 15 = 675\)
So:
\(652.50 < 450 + 8A < 675\)
\(202.50 < 8A < 225\)
\(25.\text{something} < A < 28.\text{something}\)
So \(A\) could be 26, 27, or 28.
Not sufficient.
(2) The total revenue from ticket sales was greater than $655 but less than $663.
So:
\(655 < 450 + 8A < 663\)
\(205 < 8A < 213\)
\(25.\text{something} < A < 26.\text{something}\)
Since \(A\) must be an integer:
\(A = 26\)
Sufficient.
Answer: B
A small theater sold only adult tickets and student tickets for one afternoon show. Each adult ticket cost $18, and each student ticket cost $10. If the theater sold 45 tickets for the show, how many adult tickets were sold?
Let \(A\) be the number of adult tickets sold. Then the number of student tickets sold was \(45 - A\).
The total revenue was:
\(18A + 10(45 - A) = 450 + 8A\)
The question asks for \(A\).
(1) The average ticket price was greater than $14.50 but less than $15.00.
Since 45 tickets were sold, the total revenue was greater than:
\(45 * 14.50 = 652.50\)
and less than:
\(45 * 15 = 675\)
So:
\(652.50 < 450 + 8A < 675\)
\(202.50 < 8A < 225\)
\(25.\text{something} < A < 28.\text{something}\)
So \(A\) could be 26, 27, or 28.
Not sufficient.
(2) The total revenue from ticket sales was greater than $655 but less than $663.
So:
\(655 < 450 + 8A < 663\)
\(205 < 8A < 213\)
\(25.\text{something} < A < 26.\text{something}\)
Since \(A\) must be an integer:
\(A = 26\)
Sufficient.
Answer: B
