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3 years ago

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A prince picked a basketful of golden apples in the enchanted orchard. On his way home, he was stopped by a troll who guarded. T

he 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?

2 answers:

Llana [10]3 years ago

4 0

Answer:

44.00

Step-by-step 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

Lelu [443]3 years ago

3 0

Answer:

Let x = total number of apples picked by the prince

x=44

Step-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-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

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Radda [10]

Answer:

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Step-by-step explanation:

To find the exact solution, find the equation for each line. And solve for x and y.

To do this, represent each equation in the slope-intercept form, y = mx + b. Where m is the slope, and b is the y-intercept.

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Substitute m = 2 and b = 7 in y = mx + b

Equation 1 would be:

✔️y = 2x + 7

✍️Equation 2 for the line that slopes downwards from left to your right:

Slope = $m = \frac{rise}{run} = -\frac{3}{1} = -3$

b = the point at which the y-axis is intercepted by the line = 1

Substitute m = -3 and b = 1 in y = mx + b

✔️Equation 2 would be:

y = -3x + 1

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✔️To solve for x, substitute y = -3x + 1 in equation 1.

y = 2x + 7

-3x + 1 = 2x + 7

Collect like terms

-3x - 2x = 7 - 1

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$x = \frac{6}{-5} = -1\frac{1}{5}$

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y = -3x + 1

$y = -3\frac{-6}{5} + 1$

$y = \frac{18}{5} + 1$

$y = \frac{18 + 5}{5}$

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<u>Explanation</u>

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Substituting x with √2

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2 years ago

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2 years ago

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3 years ago

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