A person needs to pay TK. 500 to by pencils and TK. X for any additinal unit of pencil. If the cumstomer pays a total of TK. 4700 for 1200 pencils what is the value of X?

Let the number of pencils bought for Tk. 500 be a and that bought for TK. X be b:

then

a+b=1200

a=1200-b ... i

500a+bx=4700 ... ii

plugging i in ii we get:

500 (1200-b) + bx=4700

600000-500b+bx=4700

595300-b (500-x) = 0

for maximum number of pencils:

d'b=0

d'b=500-x=0

thus

x=500