In May, Kylie and Japheth had buttons in the ratio 5 : 4. In June, each of them gave away the same number of buttons. Kylie then had thrice as many buttons as Japheth.

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

	Kylie	Japheth	Difference
Before	5x2 = 10 u	4x2 = 8 u	1x2 = 2 u
Change	- 7 u	- 7 u
After	3x1 = 3 u	1x1 = 1 u	2x1 = 2 u

(a)
Since Kylie and Japheth gave away the same number of buttons, the difference in the number of buttons between Kylie and Japheth 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 1 and 2 is 2.

Japheth's buttons in May : Japheth's buttons in June
8 : 1

(b)
Total number of buttons in May
= 10 u + 8 u
= 18 u

Total number of buttons in June
= 3 u + 1 u
= 4 u

Total buttons in May : Total buttons in June
18 : 4 _(÷2)
9 : 2 

Answer(s): (a) 8 : 1; (b) 9 : 2