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07 Dec 2017, 21:20
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95% (hard)

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 _________________ Senior PS Moderator Joined: 26 Feb 2016 Posts: 3332 Location: India GPA: 3.12 A store purchased x sweaters for a total price of$750. If it sold all  [#permalink]

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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] ### Show Tags 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

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] ### Show Tags 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.

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

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