Call x the number of cards of Nigel, y the number of cards of Angusand z the number of cards of Albert
you want to find x + y + z.
You know
1) x/y = 3/4 => y = (4/3)x
2) x/z = 3/5 => z = (5/3)x
3) y/z = 4/5 => y = (4/5)z
4) x = z - 14
From 1 and 3: (4/3)x = (4/5)z => x = (3/5)z
5) Replacing x = (3/5)z in x = x - 14:
(3/5)z = z - 14
=> z - (3/5)z = 14
=> (2/5)z = 14
=> z = 14*5 / 2 = 35
=> x = (3/5)*35 = 21
=> y = (4/5)*35 = 28
=> x + y + z = 21 + 28 + 35 = 84
Answer: 84
