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# S95-24

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Math Expert
Joined: 02 Sep 2009
Posts: 47168
S95-24  [#permalink]

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16 Sep 2014, 01:49
00:00

Difficulty:

45% (medium)

Question Stats:

76% (02:06) correct 24% (02:18) wrong based on 72 sessions

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An amusement park currently charges the same price for each ticket of admission. If the current price of admission were to be increased by $$3$$, 12 fewer tickets could be bought for $$160$$, excluding sales tax. What is the current price of each ticket?

A. $$3$$
B. $$5$$
C. $$8$$
D. $$20$$
E. $$32$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 47168
Re S95-24  [#permalink]

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16 Sep 2014, 01:49
Official Solution:

An amusement park currently charges the same price for each ticket of admission. If the current price of admission were to be increased by $$3$$, 12 fewer tickets could be bought for $$160$$, excluding sales tax. What is the current price of each ticket?

A. $$3$$
B. $$5$$
C. $$8$$
D. $$20$$
E. $$32$$

The question asks us to determine the current price of each ticket of admission.

If we let $$p$$ equal the current price per ticket, and $$n$$ equal the number of tickets that can be bought for $$160$$, we can set up some equations. First, we know that $$pn = 160$$.

Second, we are told that if $$p$$ is increased by 3, then 12 fewer tickets can be bought with $$160$$. This equation also expresses how many tickets can be bought for $$160$$, giving us: $$(p + 3)(n - 12) = 160$$.

Solve the first equation for $$n$$, giving: $$n = \frac{160}{p}$$.

Substitute this value for $$n$$ into the second equation, solving for $$p$$:

$$(p + 3)(\frac{160}{p} - 12) = 160$$

Multiply both sides by $$p$$ to get rid of the fraction: $$(p + 3)(\frac{160}{p} - 12)p = (p + 3)(160 - 12p) = 160p$$.

Multiply through to get rid of the parentheses: $$160p - 12p^2 + 480 - 36p = 160p$$.

Combine like terms: $$124p - 12p^2 + 480 = 160p$$. Set the equation equal to 0: $$0 = 12p^2 + 36p - 480$$.Divide both sides by 12: $$0 = p^2 + 3p - 40$$.

Factor: $$0 = (p - 5)(p + 8)$$.

Therefore, $$p = 5$$ or $$p = -8$$. Since the the price cannot be negative, $$p = 5$$.

Answer: B
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Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: S95-24  [#permalink]

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10 Jul 2015, 11:35
1
I did it by using the answer choices. I will only show it for B, the correct answer.

If the initial price was 5, then 160/5 = 32 tickets.
If the initial price is increased by 3, then 160/8 = 20 tickets.

32 - 20 = 12 fewer tickets.
Intern
Joined: 19 Sep 2016
Posts: 1
Re: S95-24  [#permalink]

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21 Sep 2016, 19:51
agreed... doing the full algebra as described here takes up a too much valuable time. you can set up the equation and plug numbers, using intuition to guide where to start
Manager
Joined: 16 Jan 2017
Posts: 65
GMAT 1: 620 Q46 V29
Re: S95-24  [#permalink]

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19 Mar 2017, 08:01
mhmmm, true it is faster. Did it the long way and i took me a bit over two minutes
Re: S95-24 &nbs [#permalink] 19 Mar 2017, 08:01
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# S95-24

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