Question

Two leprechauns are arguing over a pot of gold. The first leprechaun says to the other, ‘Give me seven of your gold pieces and I will have twice as many as you!’, the other one replies, ‘No way! Give me seven of yours and we’ll have the same number’. How many gold pieces does the first leprechaun have?

Answer 1

Gold pieces the first leprechaun has: x
Gold pieces the second leprechaun has: y

The first leprechaun says to the other, ‘Give me seven of your gold pieces and I will have twice as many as you!’:
The first leprechaun would have x+7
The second leprechaun would have y-7
I will have twice as many as you:
(1) x+7=2(y-7)
(1) x+7=2y-14
(1) x+7-7-2y=2y-14-7-2y
(1) x-2y=-21

The other one replies, ‘No way! Give me seven of yours and we’ll have the same number’
The first leprechaun would have x-7
The second leprechaun would have y+7
We’ll have the same number:
(2) x-7=y+7
(2) x-7+7-y=y+7+7-y
(2) x-y=14

How many gold pieces does the first leprechaun have?
x=?
We have a system with 2 equations and two unknows (x and y). We need to solve for x:
(1) x-2y=-21
(2) x-y=14

Using the method of substitution, we can isolating y in the second equation:
(2) x-y=14
(2) x-y+y-14=14+y-14
(2) x-14=y
(2) y=x-14  

And we can replace y in the first equation by x-14, and solve for x: 
(1) x-2y=-21
(1) x-2(x-14)=-21
(1) x-2x+28=-21
(1) -x+28=-21
(1) -x+28-28=-21-28
(1) -x=-49
(1) (-1)*(-x=-49)
(1) x=49

Answer: The first leprechaun has 49 gold pieces