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A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener

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Math Expert
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A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener  [#permalink]

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01 Dec 2014, 04:32
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:59) correct 17% (03:03) wrong based on 59 sessions

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Tough and Tricky questions: Word Problems.

A snooker tournament charges \$45.00 for VIP seats and \$15.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of \$7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?

A) 70
B) 90
C) 140
D) 230
E) 250

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener  [#permalink]

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01 Dec 2014, 04:59
let x be the number of VIP seats tickets sold and y be the number of general seats tickets sold.

x+y=320 ....... 1
45x+15y=7500 ......... 2

Divide eq 2 by 15
3x+y=500 ......... 3

eq3- eq1
2x=180
x=90

therefore, y=320-90
y=230

y-x= 230-90=140

Ans - C
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Re: A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener  [#permalink]

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01 Dec 2014, 17:11
This was a simultaneous equations question for me. Let v = VIP tickets and g = general admission.
We know that v + g = 320 (320 total tickets sold) and 45v + 15g = 7500 (total cost of all the tickets. Now, lets reduce this second equation to make things easier by dividing it by 15: 3v + g = 500.

Let's do equation 2 - equation 1 to get (3v-v) + (g-g) = 500-320, this yields 2v = 180 or v = 90 (90 VIP tickets sold), which means that 320-90=g=230 general admission tickets sold. The difference is 140, which is Choice C.
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Re: A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener  [#permalink]

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01 Dec 2014, 18:07
1

................. VIP ..................... Regular .................. Total

Price ........ 45 ......................... 15 ......................... 7500 (Total Amount)

Quantity ...... x ........................ 320-x ......................... 320 (Total sale)

We require to find 320-x-x = 320 - 2x

45x + 15(320-x) = 7500

x = 90

320 - 2x = 320 - 180 = 140
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Re: A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener  [#permalink]

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01 Dec 2014, 18:31
2
My method is a little bit different, but it works fairly fast if you know how to do it.

If all the tickets sold were the \$45 tickets, the amount would be \$14,400.
If all the tickets sold were the \$15 tickets, the amount would be \$4,800.

You can then use the ratio trick to determine what the proper ratio should be for the total amount to equal \$7,500:

4,800 --- 7,500 --- 14,400

The difference between those numbers and the 7,500 amount is 2,700 (7,500-4,800) and 6,900 (14,400-7,500). That means the ratio of \$15 tickets to \$45 tickets should be 6900:2700 (you flip the differences).

6900:2700 reduces to 69:27, which reduces to 23:9. To get 320 tickets sold, multiply by 10 to get 230:90. 230-90 = 140, which is the answer.

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Re: A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener  [#permalink]

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01 Dec 2014, 21:08
VIP = V and General =G
Given V + G = 320 ---Eq1
and 45V + 15G = 7500 ---Eq2
Solving Eq1 and Eq2 => V= 90 , G =230 and G-V = 140.

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Joined: 02 Sep 2009
Posts: 64249
Re: A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener  [#permalink]

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02 Dec 2014, 08:01
Bunuel wrote:

Tough and Tricky questions: Word Problems.

A snooker tournament charges \$45.00 for VIP seats and \$15.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of \$7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?

A) 70
B) 90
C) 140
D) 230
E) 250

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener  [#permalink]

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21 Mar 2020, 07:32
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Re: A snooker tournament charges \$45.00 for VIP seats and \$15.00 for gener   [#permalink] 21 Mar 2020, 07:32