In April, Xuan and Ahmad had buttons in the ratio 9 : 4. In May, each of them gave away the same number of buttons. Xuan then had five times as many buttons as Ahmad.

1. Find the ratio of the number of buttons Ahmad had in April to the number of buttons he had in May.
2. Find the ratio of the total number of buttons both had in April to the total number of buttons both had in May.

	Xuan	Ahmad	Difference
Before	9x4 = 36 u	4x4 = 16 u	5x4 = 20 u
Change	- 11 u	- 11 u
After	5x5 = 25 u	1x5 = 5 u	4x5 = 20 u

(a)
Since Xuan and Ahmad gave away the same number of buttons, the difference in the number of buttons between Xuan and Ahmad at first and in the end remains the same.

Make the difference in the number of buttons at first and in the end the same. LCM of 5 and 4 is 20.

Ahmad's buttons in April : Ahmad's buttons in May
16 : 5

(b)
Total number of buttons in April
= 36 u + 16 u
= 52 u

Total number of buttons in May
= 25 u + 5 u
= 30 u

Total buttons in April : Total buttons in May
52 : 30 _(÷2)
26 : 15 

Answer(s): (a) 16 : 5; (b) 26 : 15