In May, Natalie and Tommy had buttons in the ratio 3 : 2. In June, each of them gave away the same number of buttons. Natalie then had four times as many buttons as Tommy.

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

	Natalie	Tommy	Difference
Before	3x3 = 9 u	2x3 = 6 u	1x3 = 3 u
Change	- 5 u	- 5 u
After	4x1 = 4 u	1x1 = 1 u	3x1 = 3 u

(a)
Since Natalie and Tommy gave away the same number of buttons, the difference in the number of buttons between Natalie and Tommy 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 3 is 3.

Tommy's buttons in May : Tommy's buttons in June
6 : 1

(b)
Total number of buttons in May
= 9 u + 6 u
= 15 u

Total number of buttons in June
= 4 u + 1 u
= 5 u

Total buttons in May : Total buttons in June
15 : 5 _(÷5)
3 : 1 

Answer(s): (a) 6 : 1; (b) 3 : 1