Let the number of large shirts be l and the number of small shirts be s.
Let the price of a small shirt be x and that of a large shirt be x + 50.
Now, s + l = 64
l (x+50) = 5000
sx = 1800
Adding them, we get,
lx + sx + 50l = 6800
64x +50l = 6800
Substituting l = (6800 - 64x) / 50, in the original equation, we get
$\frac{(6800−64x)}{50}$(x+50)=5000
(6800 - 64x)(x + 50) = 250000
$6800x+340000−64x^2−3200x=250000$
$64x^2−3600x−90000=0$
Solving, we get, x= $\frac{225±375}8 = \frac{600}{8} or −\frac{150}8$
SO, x = 75
x + 50 = 125
Answer = 75 + 125 = 200.
Alternate approach: By options.
Hint: Each option gives the sum of the costs of one large and one small shirt. We know that large = small + 50
Hence, small + small + 50 = option.
SMALL = (Option - 50)/2
LARGE = Small + 50 = (Option + 50)/2
Option A and Option D gives us decimal values for SMALL and LARGE, hence we will consider them later.
Lets start with Option B.
Large = 150 + 50 / 2 = 100
Small = 150 - 50 / 2 = 50
Now, total shirts = 5000/100 + 1800/50 = 50 + 36 = 86 (X - This is wrong)
Option C -
Large = 200 + 50 / 2 = 125
Small = 200 - 50 / 2 = 75
Total shirts = 5000/125 + 1800/75 = 40 + 24 = 64 ( This is the right answer)
