Since bc=2 and ab=1 then bc-ab has to equal ab.
If you factorize bc-ab you get b(c-a)=ab
Dividing both sides by b gives you c-a=a
Therefore c=2a
Then I saw that cd= bc + ab (because cd=3, bc=2 and ab=1)
So substituting in what we learnt previously we get
2ad= 2ab+ab which equals 2ad=3ab
If we now divide both sides by a we get 2d=3b
And if we now divide both sides by 2 to get d alone we get 1.5b= d
Next I saw de=4 and bc=2 so de-bc=bc
Since c=2a and d=1.5b, 1.5be-2ab=2ab
so 1.5be= 4ab now we can divide both sides by b so
1.5e=4a, from here we can divide both sides by 4 to get a
.375e = a
Since ea=6 and a=.375e, e*.375e=6
So .375e^2 = 6
Dividing both sides by .375 we find that e^2=16
So e=4
Since .375e = a
.375 *4=a, so a = 1.5
Since c=2a, c=3
Since cd=3 and de=4, d=1
Since ab=1 and a=1.5, 1/1.5=b, b=2/3
Since bc=2, and c =3 and b= 2/3, bc does =2 proving this correct.
To recap,
a=1.5
b=2/3
c=3
d=1
e=4