You have 4 3/7 grams of a substance and want to divide it into vials of 6 1/4 grams each. estimate how many vials you can fill.

vials

Step-by-step explanation:

You have = grams of a substance.

You want to divide it into vials of = grams each.

Number of vials you can fill is:   ÷ = × = vials

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