Question

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 1

44.00

Explanation:

Number of Apple's left after meeting 1st troll

Y = z - (1/2z + 2)

Y =1/2z - 2 ...equ1

Number of Apple's left after meeting 2nd troll = D

D = Y - (1/2Y + 2)...equ2

Sub Y into equ 2

D = 1/4 z -3

Equation of Apple's left after meeting 3rd troll

2 = D - (1/2 D + 2)...equ 3

Sub D into equ3

2 = 1/8 z - 3 +(3/2) -2

2 = 1/8z - 5 + (3/2)....Equation 4

Multiply equ4 by 8

16 = z - 40 + 12

Z = 44.00 apples

Answer 2

Let x = total number of apples picked by the prince

x=44

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-1

0.25x-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)=2

0.25x-3- 0.125x-0.5=2

0.125x-3.5=2

0.125x =2+3.5

0.125x=5.5

x=5.5/0.125 (divide both sides by 0.125)

=44 apples

Therefore total number of apples picked by the prince, x=44