In May, Hazel and Reggie had buttons in the ratio 15 : 7. In June, each of them gave away the same number of buttons. Hazel then had four times as many buttons as Reggie.

1. Find the ratio of the number of buttons Reggie 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.

	Hazel	Reggie	Difference
Before	15x3 = 45 u	7x3 = 21 u	8x3 = 24 u
Change	- 13 u	- 13 u
After	4x8 = 32 u	1x8 = 8 u	3x8 = 24 u

(a)
Since Hazel and Reggie gave away the same number of buttons, the difference in the number of buttons between Hazel and Reggie 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 8 and 3 is 24.

Reggie's buttons in May : Reggie's buttons in June
21 : 8

(b)
Total number of buttons in May
= 45 u + 21 u
= 66 u

Total number of buttons in June
= 32 u + 8 u
= 40 u

Total buttons in May : Total buttons in June
66 : 40 _(÷2)
33 : 20 

Answer(s): (a) 21 : 8; (b) 33 : 20