In April, Elyse and Valen had buttons in the ratio 7 : 6. In May, each of them gave away the same number of buttons. Elyse then had five times as many buttons as Valen.

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

	Elyse	Valen	Difference
Before	7x4 = 28 u	6x4 = 24 u	1x4 = 4 u
Change	- 23 u	- 23 u
After	5x1 = 5 u	1x1 = 1 u	4x1 = 4 u

(a)
Since Elyse and Valen gave away the same number of buttons, the difference in the number of buttons between Elyse and Valen 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 4 is 4.

Valen's buttons in April : Valen's buttons in May
24 : 1

(b)
Total number of buttons in April
= 28 u + 24 u
= 52 u

Total number of buttons in May
= 5 u + 1 u
= 6 u

Total buttons in April : Total buttons in May
52 : 6 _(÷2)
26 : 3 

Answer(s): (a) 24 : 1; (b) 26 : 3