Gerald went to a bake sale and found a pan of brownies that had ⅖ of the brownies remaining. He asked to buy ⅓ of the remaining brownies. Marlon said that Gerald bought 29 of the pan. Gerald says that Marlon made a mistake. Identify Marlon’s error, and share what the actual answer would be.

instead of  2/9 he put 29

Step-by-step explanation:

he put 29 instead of 2/9.

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