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A movie hall sold tickets to one of its shows in two denominations, $11 and $7. A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall. If the total collections from tickets and refreshments for the show was $124, how many $7 tickets were sold? Note: The number of $11 tickets sold is different from the number of $7 tickets sold.
  • a)
    14
  • b)
    11
  • c)
    2
  • d)
    8
  • e)
    5
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
A movie hall sold tickets to one of its shows in two denominations, $1...
Assign Variables | Frame Equations
Let ‘x’ and ‘y’ be the number of tickets sold at $11 and $7 respectively.
Then, total number of tickets sold = x + y
Collection by selling 'x' $11 tickets = 11x
Collection by selling 'y' $7 tickets = 7y
Total collection by selling (x + y) tickets = 11x + 7y
A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall.
i.e., 1414(x + y) spent $4 on refreshments.
∴ Collections from sale of refreshments = 1414(x + y) × 4 = (x + y)
Total collection from tickets and refreshments = $124
i.e., 11x + 7y + (x + y) = 124
Or 12x + 8y = 124
Divide the equation by 4: 3x + 2y = 31
Solve 3x + 2y = 31 for x and y using these 2 facts
Fact 1: x and y are positive integers.
Fact 2: 1414 (x + y) is an integer because a fourth of total tickets sold should be an integer. i.e., (x + y) should be a multiple of 4.
Let us list down the different possibilities that satisfy the equation and fact 1
Of all the different positive integer values of x and y that satisfy the equation, the only combination (x, y) = (7, 5) is divisible by 4
So, the movie hall sold five $7 tickets.
Choice E is the correct answer.
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Most Upvoted Answer
A movie hall sold tickets to one of its shows in two denominations, $1...
Assign Variables | Frame Equations
Let ‘x’ and ‘y’ be the number of tickets sold at $11 and $7 respectively.
Then, total number of tickets sold = x + y
Collection by selling 'x' $11 tickets = 11x
Collection by selling 'y' $7 tickets = 7y
Total collection by selling (x + y) tickets = 11x + 7y
A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall.
i.e., 1414(x + y) spent $4 on refreshments.
∴ Collections from sale of refreshments = 1414(x + y) × 4 = (x + y)
Total collection from tickets and refreshments = $124
i.e., 11x + 7y + (x + y) = 124
Or 12x + 8y = 124
Divide the equation by 4: 3x + 2y = 31
Solve 3x + 2y = 31 for x and y using these 2 facts
Fact 1: x and y are positive integers.
Fact 2: 1414 (x + y) is an integer because a fourth of total tickets sold should be an integer. i.e., (x + y) should be a multiple of 4.
Let us list down the different possibilities that satisfy the equation and fact 1
Of all the different positive integer values of x and y that satisfy the equation, the only combination (x, y) = (7, 5) is divisible by 4
So, the movie hall sold five $7 tickets.
Choice E is the correct answer.
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Community Answer
A movie hall sold tickets to one of its shows in two denominations, $1...
Let's assume the number of $11 tickets sold is 'x' and the number of $7 tickets sold is 'y'.

Given that the total collections from tickets and refreshments for the show was $124, we can set up the following equation:
11x + 7y + 4(1/4)(x + y) = 124

Simplifying the equation, we get:
11x + 7y + x + y = 124
12x + 8y = 124
3x + 2y = 31

Since the number of $11 tickets sold is different from the number of $7 tickets sold, we know that x is not equal to y. Therefore, we can assume that x > y.

Now, let's examine the possible values of x and y to solve the equation.

Assume x = 1. In this case, 3(1) + 2y = 31
Simplifying the equation, we get:
2y = 28
y = 14

Therefore, if x = 1, y = 14. However, this does not satisfy the condition that x is not equal to y.

Assume x = 2. In this case, 3(2) + 2y = 31
Simplifying the equation, we get:
2y = 25
y = 12.5

Since y cannot be a decimal, this assumption is not valid.

Assume x = 3. In this case, 3(3) + 2y = 31
Simplifying the equation, we get:
2y = 22
y = 11

Therefore, if x = 3, y = 11. This satisfies the condition that x is not equal to y.

Hence, the number of $7 tickets sold is 11. Option E is the correct answer.
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A movie hall sold tickets to one of its shows in two denominations, $11 and $7. A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall. If the total collections from tickets and refreshments for the show was $124, how many $7 tickets were sold? Note: The number of $11 tickets sold is different from the number of $7 tickets sold.a)14b)11c)2d)8e)5Correct answer is option 'E'. Can you explain this answer?
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A movie hall sold tickets to one of its shows in two denominations, $11 and $7. A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall. If the total collections from tickets and refreshments for the show was $124, how many $7 tickets were sold? Note: The number of $11 tickets sold is different from the number of $7 tickets sold.a)14b)11c)2d)8e)5Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A movie hall sold tickets to one of its shows in two denominations, $11 and $7. A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall. If the total collections from tickets and refreshments for the show was $124, how many $7 tickets were sold? Note: The number of $11 tickets sold is different from the number of $7 tickets sold.a)14b)11c)2d)8e)5Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A movie hall sold tickets to one of its shows in two denominations, $11 and $7. A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall. If the total collections from tickets and refreshments for the show was $124, how many $7 tickets were sold? Note: The number of $11 tickets sold is different from the number of $7 tickets sold.a)14b)11c)2d)8e)5Correct answer is option 'E'. Can you explain this answer?.
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