Question

Nigel, Angus, and Albert bought packs of hockey cards and split them in a ratio of 3:4:5. Nigel has 14 fewer cards than Albert. How many cards did the boys have in total?

Answer 1

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