If you picked 41.5% of the apples on a tree, and you picked 34 apples, how many apples did the tree contain before you starting picking?

81.9 apples (= 82 apples rounded to nearest whole number)

Step-by-step explanation:

41.5% > represents 34 apples

1% > represents (34 / 41.5) apples

100% > represents (34 / 41.5) x 100 apples= 81.9 apples (= 82 apples rounded to nearest whole number)

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