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The total cost of a vacation was divided equally among 3 people. If

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The total cost of a vacation was divided equally among 3 people. If  [#permalink]

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New post Updated on: 08 Oct 2019, 07:16
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The total cost of a vacation was divided equally among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost of the vacation?

A. $200
B. $300
C. $400
D. $500
E. $600

Originally posted by blog on 31 Jan 2008, 20:00.
Last edited by Bunuel on 08 Oct 2019, 07:16, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: The total cost of a vacation was divided equally among 3 people. If  [#permalink]

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New post 31 Jan 2008, 21:33
blog wrote:
The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?

1. $200
2. $300
3. $400
4. $500
5. $600


x/3=c x/4=c-50 ---> x/4=x/3-50 ---> x/4-x/3=-50 --> -x/12=-50 --> x=600


E
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Re: The total cost of a vacation was divided equally among 3 people. If  [#permalink]

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New post 31 Jan 2008, 21:45
x/4=x/3-50 where x is total cost of vacation

x=600
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Re: The total cost of a vacation was divided equally among 3 people. If  [#permalink]

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New post 16 Jan 2016, 07:23
C for cost.
P price per person.
C= 3*P
C-200=4*P

Substituting the value of P from the first equation onto the second we get P = 200.
Plugging in the value of P in the first equation, we get C= 600. Which leads us to answer choice E
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Re: The total cost of a vacation was divided equally among 3 people. If  [#permalink]

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New post 17 Jan 2016, 21:17
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Hi All,

This question can be solved by TESTing THE ANSWERS. There are also some logical 'shortcuts' in the design of this question that you can take advantage of.

We're told that the total cost of a vacation was divided among 3 PEOPLE. We're then told that if the total cost of the vacation had been divided equally among 4 PEOPLE, then the cost per person would have been $50 LESS. We're asked for the total cost of the vacation.

Looking at the answer choices, we can see that they're all 'nice' round numbers. Since the total cost was originally going to be divided among 3 people, that cost is almost certainly going to be a multiple of 3. Only answers B and E fit that pattern.

Let's TEST Answer B: $300

IF.... Total Cost = $300
Cost for 3 people = $100 each
Cost for 4 people = $75 each
Difference = $25
This is NOT a match for what we were told (the difference is supposed to be $50).
Eliminate Answer B.

Notice how $25 is exactly HALF of $50 though.... Maybe we need to DOUBLE all of the values....

Let's TEST Answer E: $600

IF.... Total Cost = $600
Cost for 3 people = $200 each
Cost for 4 people = $150 each
Difference = $50
This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:

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Re: The total cost of a vacation was divided equally among 3 people. If  [#permalink]

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New post 24 Jan 2019, 06:46
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blog wrote:
The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?

A. $200
B. $300
C. $400
D. $500
E. $600


Let T = total cost of vacation
So, T/3 = cost per person with THREE people
And T/4 = cost per person with FOUR people

If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less.
In other words (cost per person with FOUR people) = (cost per person with THREE people) - $50
We can write: T/4 = T/3 - 50

At this point, we can EITHER test the answer choices OR solve the equation.
Let's solve the equation.

Take: T/4 = T/3 - 50
12 is the LCM of 3 and 4, so multiply both sides by 12 to get: 3T = 4T - 600
Solve: T = 600

Answer: E

Cheers,
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Re: The total cost of a vacation was divided equally among 3 people. If  [#permalink]

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New post 24 Jan 2019, 07:13
blog wrote:
The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?

A. $200
B. $300
C. $400
D. $500
E. $600

\(? = 12T\,\,\,\,\left[ \$ \right]\)

\({\text{per}}\,\,{\text{person}}\,\,\,:\,\,\,\frac{{12T}}{3} = \frac{{12T}}{4} + 50\,\,\,\,\, \Rightarrow \,\,\,T = 50\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 600\,\,\,\,\left[ \$ \right]\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: The total cost of a vacation was divided equally among 3 people. If  [#permalink]

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New post 24 Jan 2019, 07:49
blog wrote:
The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?

A. $200
B. $300
C. $400
D. $500
E. $600


\(\frac{x}{3} - \frac{x}{4} = 50\)

So, We know that x must be completely divisible by both 3 & 4

Least possible value of x is LCM of 3 & 4 = 12

Now, Check the options, Only (E) 600 is divisible by 12, thus Answer must be (E)
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Re: The total cost of a vacation was divided equally among 3 people. If  [#permalink]

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New post 01 Feb 2019, 18:34
blog wrote:
The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?

A. $200
B. $300
C. $400
D. $500
E. $600


We let x = the total cost of the vacation and create the equation:

x/4 = x/3 - 50

Multiplying both sides of the equation by 12, we have:

3x = 4x - 600

600 = x

Answer: E
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Re: The total cost of a vacation was divided equally among 3 people. If   [#permalink] 01 Feb 2019, 18:34
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