RatioStructured · 4 marks

There were some stamps in Album M and Album N. Ahmad moved 14 of the stamps from Album M into Album N. As a result, the ratio of the number of stamps in Album M to the number in Album N became 2 : 5. Album N then had 216 more stamps than Album M.

What was the ratio of the number of stamps in Album M to the number in Album N at first?
How many stamps were there in Album N at first?

Need a hint?

Find the difference in units after the move first, then work backwards: how many stamps did Album M lose, and what did Album N gain?

Worked answer

(a) After the move, Album M : Album N = 2 : 5, so the difference is 3 units.
(a) 3 units = 216, so 1 unit = 72.
(a) After the move, Album M has 2 units = 144 stamps, and Album N has 5 units = 360 stamps.
(a) Album M after the move is 3 parts of its original 4 parts, so 1 part = 144 ÷ 3 = 48 stamps.
(a) Original Album M = 4 parts = 192 stamps, so the moved stamps (1 part) = 48.
(a) Original ratio: Album M : Album N = 192 : 312 = 8 : 13.
(b) Album N after = 360, and it received 48 stamps, so original Album N = 360 − 48 = 312.

Answer: 312 stamps

Habit

Students often read the ratio 2 : 5 as the original ratio, or add the moved stamps to Album M instead of Album N.