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

Question

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

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

pushpitkc · Answer

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)

arvind910619 · Answer

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
5 x^2 - 50 x - 3000 = 0

Solving this we get x=30
he sold 30-4 =26 sweaters

ScottTargetTestPrep · Answer

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

The store sold (x - 4) sweaters for   each and made a profit of 30 dollars; thus:

(x - 4)  - 750 = 30

(x - 4)  = 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

TheNightKing · Answer

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.

EgmatQuantExpert · Answer

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

EgmatQuantExpert · Answer

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

AnuK2222 · Answer

they always get you when you think its easy and doable in less than 2 minutes :'(

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

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