To get a certain shade of green plant. melissa decides to mix 3 gallons of blue paint with 2 gallons of yellow paint. how much blue paint does melissa need for each gallon of yellow paint?

Well seeing as the ratio is 3 gallons of blue paint to every 2 gallons of yellow paint, for every one gallon of yellow paint she would need 1.5 gallons of blue paint.

Also 3 divided by 2 is 1.5 but either way is fine I think

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