Ryan has nine 14 - ounce bags of popcorn to repackage and sell at the school fair. a small bag holds 3 ounces. how many small bags can he make

42

Explanation:

If he has nine 14 ounce bags, that would mean that he has  

9

×

14

=

126

ounces of the popcorn

Therefore, we can divide 126 by 3 (the capacity of a small bag).

126

÷

3

=

42

So, he has 42 small bags of popcorn.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4