A pup is worth a pooch and a mutt. A pup and a pooch are worth one bird dog. Two bird dogs are worth three mutts.
how many pooches is a pup worth?
w= pup
x= pooch
y = mutt
z = bird dog
w = x + y (1)
z = w + x ⇒ (2/3) z = (2/3) w + (2/3)x (2)
2z = 3y (3)
Relate w and x
Manipulate (3)
y = (2/3)z
Put this into (1) for y
w = x + (2/3)z
Sub (2) into (1)
w = x + [ (2/3)w + (2/3)x ] rearrange as
w - (2/3)w = x + (2/3) x
(1/3)w = (5/3)x
w = 5x
1 pup = 5 pooches