A prince picked a basketful of golden apples in the enchanted orchard. On his way home, he was stopped by a troll who guarded. The troll demanded payment of 1/2 of the apples plus two more. The prince gave him the apples and set off. A little further on, he was stopped by a second troll guard who demanded a payment of 1/2 of the apples the prince now had plus two more. The prince paid and set off again. Just before leaving the orchard, a third troll stopped him demanding 1/2 of his remaining apples plus two more. Sadly, the prince paid him and went home. He had only two golden apples left. How many apples had he picked?

Answer:Let x = total number of apples picked by the princex=44Step-by-step explanation:1st troll payment x-(0.5x+2) x-0.5x-2 0.5x-2 (that is the amount of apples left after 1st troll payment) 2nd troll payment (0.5x-2)-(0.5(0.5x-2)+2)Simplifying,(0.5x-2)-(0.25x-1+2)(0.5x-2)-(0.25x+1)0.5x-2-0.25x-10.25x-3 (apples remaining after 2nd troll payment)3rd troll payment (0.25x-3)-(0.5(0.25x-3)+2)=2(0.25x-3)-(0.125x-1.5+2)=2(0.25x-3)-(0.125x+0.5)=20.25x-3- 0.125x-0.5=20.125x-3.5=20.125x =2+3.50.125x=5.5x=5.5/0.125 (divide both sides by 0.125)=44 applesTherefore total number of apples picked by the prince, x=44