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A store purchased x sweaters for a total price of $750. If it sold all

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A store purchased x sweaters for a total price of $750. If it sold all  [#permalink]

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New post 07 Dec 2017, 20:20
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A store purchased x sweaters for a total price of $750. If it sold all but four of them, each for $5 more than the average price it paid for a sweater, and in doing so earned a total profit of $30 on the original purchase, how many sweaters did it sell?

A. 21
B. 24
C. 26
D. 30
E. 35

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A store purchased x sweaters for a total price of $750. If it sold all  [#permalink]

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New post 07 Dec 2017, 22:05
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This easiest solution for this problem is to work with the answer options

If n is the average price per sweater from the question stem,
we can form the following equations :

nx = 750
(x-4)(n+5) = 750+30 = 780

Lets evaluate answer Option C, x-4 = 26, because it divides 780 without a remainder.
Therefore, n+5 = 780/26 = 30
To cross check if the answer is correct x-4 = 26, x=30 and n = 30-5 = making the selling price(26*30 = 780)

Since we have been asked to find the total number of sweaters sold, it must be (x-4=26) (Option C)

Alternate approach:

nx = 750 -> (1)
(x-4)(n+5) = 780 -> (2)

nx - 4n + 5x - 20 = 780
Substutiting nx=750 from (1)
5x - 4n = 800 - 750 = 50 -> (3)

From (1), we can deduce n = \(\frac{750}{x}\)

\(5x - \frac{3000}{x} - 50 = 0\)
\(5x^2 - 50x - 3000 = 0\)

Solving for x, x=- 50 and 60(x cannot be negative)

Therefore, the number of sweaters sold is 26(Option C)
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Re: A store purchased x sweaters for a total price of $750. If it sold all  [#permalink]

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New post 07 Dec 2017, 22:33
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Bunuel wrote:
A store purchased x sweaters for a total price of $750. If it sold all but four of them, each for $5 more than the average price it paid for a sweater, and in doing so earned a total profit of $30 on the original purchase, how many sweaters did it sell?

A. 21
B. 24
C. 26
D. 30
E. 35


The answer is 26

X sweaters are purchased for 750 then price per sweater is 750/x

He sold all but 4 means that he sold x-4 for a prices greater than 750/x by 5
He earned a profit of 30
So putting the in equation we have

(x-4)(750/x+5)-750=30

or
5x^2-10x-600=0

Solving this we get x=30
he sold 30-4 =26 sweaters
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Re: A store purchased x sweaters for a total price of $750. If it sold all  [#permalink]

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New post 01 Feb 2019, 17:45
Bunuel wrote:
A store purchased x sweaters for a total price of $750. If it sold all but four of them, each for $5 more than the average price it paid for a sweater, and in doing so earned a total profit of $30 on the original purchase, how many sweaters did it sell?

A. 21
B. 24
C. 26
D. 30
E. 35


The average price paid for each sweater is 750/x.

The store sold (x - 4) sweaters for [(750/x) + 5 dollars] each and made a profit of 30 dollars; thus:

(x - 4)[(750/x) + 5] - 750 = 30

(x - 4)[(750/x) + (5x/x)] = 780

(x - 4)(750 + 5x)/x = 780

750x + 5x^2 - 3000 - 20x = 780x

5x^2 - 50x - 3000 = 0

x^2 - 10x - 600 = 0

(x - 30)(x + 20) = 0

x = 30 or x = -20

Since x can’t be negative, x = 30. So the store purchased 30 sweaters and sold 26 of them.

Answer: C
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Re: A store purchased x sweaters for a total price of $750. If it sold all   [#permalink] 01 Feb 2019, 17:45
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