In March, Tammy and Ethan had buttons in the ratio 12 : 5. In April, each of them gave away the same number of buttons. Tammy then had thrice as many buttons as Ethan.

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

	Tammy	Ethan	Difference
Before	12x2 = 24 u	5x2 = 10 u	7x2 = 14 u
Change	- 3 u	- 3 u
After	3x7 = 21 u	1x7 = 7 u	2x7 = 14 u

(a)
Since Tammy and Ethan gave away the same number of buttons, the difference in the number of buttons between Tammy and Ethan 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 7 and 2 is 14.

Ethan's buttons in March : Ethan's buttons in April
10 : 7

(b)
Total number of buttons in March
= 24 u + 10 u
= 34 u

Total number of buttons in April
= 21 u + 7 u
= 28 u

Total buttons in March : Total buttons in April
34 : 28 _(÷2)
17 : 14 

Answer(s): (a) 10 : 7; (b) 17 : 14