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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, 21:20
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A
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C
D
E

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Question Stats:

56% (02:50) correct 44% (03:10) wrong based on 81 sessions

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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, 23:05
1
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, 23:33
1
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, 18:45
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]

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New post 28 Sep 2019, 09:48
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


\(Cost Price of Each =750/(Number of Sweaters sold+4)\)

Options:
A. \(750/25\)
B. \(750/28\)
C. \(750/30\)
D. \(750/34\)
E. \(750/39\)

B,D and E are not possible.

You can either try A or C. I tried C first.

C gives a cost price of 25. So 26 were sold at 30$ which gives us 780$ and technically the cost price is already given as 750$ so the profit is indeed 30$.

Hence 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 29 Sep 2019, 07:11

Solution



Given

    • A store purchased x sweaters.
    • Total cost price of sweaters = $750
    • The store sold all the sweaters but four of them.
      o The sales price of each sweater is $5 more than the cost price of each sweater.
    • The profit of the store is $30.

To find
    • The number of sweaters the store sold.

Approach and Working out

Let the store purchased x sweaters.
    • So, cost price of each sweater = $750/x
Total sweaters bought = x-4 and total selling price = $780
    • So, selling price of each sweater = $780/x-4
The sales price of each sweater is $5 more than the cost price of each sweater.
    • Selling price of each sweater – Cost price of each sweater = 5
    • $780/(x-4) - $750/x = 5
    • 156/(x-4) - 150/x = 1

Method -1
Solve the equation.
    • 156/(x-4) - 150/x = 1
    • 156x – 150(x-4) = x(x-4)
    • 6x +600 = x^2 – 4x
    • 600 = x^2 – 10 x =x (x-10)
    • 60* 10 = 15 * 4 *10 = 30 * 20 =x (x-10)
    • Hence, x = 30

So, the store sold 26 sweaters.

Hence, option C is the correct answer.

Correct Answer: 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 29 Sep 2019, 07:16
Method -2

Be a little smart

• 156/(x-4) - 150/x = 1
• 150 is a multiple of 10 or 5. So, try to pick values that are multiple of 5 or 10.
o So, 30 or 35 can be the values of x.
o x - 4 = 26
• 156 / 26 – 150/30 = 6 – 5 = 1
So, x = 30
So, the store sold 26 sweaters.

Hence, option C is the correct answer.

Correct Answer: Option C
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Re: A store purchased x sweaters for a total price of $750. If it sold all   [#permalink] 29 Sep 2019, 07:16
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