Michelle had a birthday party. she bought a bag of candy with 96 starbursts, 72 hershey’s, and 68 reese’s. if she wants to make goodie bags with the same amount of starbursts, hershey’s and reese’s in each bag, what is the largest number of bags she can make?

f

step-by-step explanation:

f

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