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A movie hall sold tickets to one of its shows in two denominations, $1

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A movie hall sold tickets to one of its shows in two denominations, $1  [#permalink]

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New post 07 Jul 2020, 11:09
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A
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C
D
E

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  85% (hard)

Question Stats:

33% (02:32) correct 67% (03:07) wrong based on 18 sessions

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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
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A movie hall sold tickets to one of its shows in two denominations, $1  [#permalink]

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New post 07 Jul 2020, 19:34
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Number of $11 tickets sold = x

Number of $7 tickets sold = y

\(11x+7y + \frac{4*(x+y)}{4} = 124\)

\(12x+8y = 124\)

\(3x+2y = 31\)

We can infer from the above equation that x is less than 10 and must be odd. If x is odd, y must be odd.

Eliminate A, C and D

If y= 11; x= 3. x+y is not a multiple of 4

Eliminate B

E



YashKothari94 wrote:
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
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Joined: 08 Mar 2020
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WE: Corporate Finance (Non-Profit and Government)
A movie hall sold tickets to one of its shows in two denominations, $1  [#permalink]

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New post 07 Jul 2020, 20:34
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1
11x + 7y + (x+y) =124
12x +8y=124
3x + 2y = 31

We are looking here for integer solutions
2x will always be even and 31 is odd
____ + even = odd
Means 3x should be odd
Means x can only take odd values only

If x= 1, y =14, x+y =15
If x= 3, y =12, x+y =15
If x= 5, y =8, x+y = 13
If x= 7, y =5, x+y =12
If x= 9, y =2, x+y =11
If x= 10, y =1/2 not possible

Also, as 1/4th of the total people buy refreshment, 1/4th of (X+y) should be an integer value means x+y should be divisble by 4.
Hence only one solution remains out of the above solutions

X=7, Y= 5

Answer is E

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A movie hall sold tickets to one of its shows in two denominations, $1   [#permalink] 07 Jul 2020, 20:34

A movie hall sold tickets to one of its shows in two denominations, $1

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