Dan sold half of his comic books and then bought 8 more. he now has 12. how many did he begin with?

Let's say Dan started out with b comic books.

He sold half of the, leaving (1/2)b books.

He then bought 8 more, so that he owned (1/2)b + 8 books, or 12 books.

Solve for b:  Subtract 8 books from both sides, obtaining (1/2)b = 4 books.

Multiplying both sides by 2, to clear the fraction, we get b = 8 books.

Dan started out with 8 books.

He sold half, leaving himself with 4 books.

Then he bought 8 more.  4 plus 8 is 12, which checks with the problem statement.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet