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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