In April, Irene and Luis had buttons in the ratio 14 : 9. In May, each of them gave away the same number of buttons. Irene then had thrice as many buttons as Luis.

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

	Irene	Luis	Difference
Before	14x2 = 28 u	9x2 = 18 u	5x2 = 10 u
Change	- 13 u	- 13 u
After	3x5 = 15 u	1x5 = 5 u	2x5 = 10 u

(a)
Since Irene and Luis gave away the same number of buttons, the difference in the number of buttons between Irene and Luis 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 5 and 2 is 10.

Luis's buttons in April : Luis's buttons in May
18 : 5

(b)
Total number of buttons in April
= 28 u + 18 u
= 46 u

Total number of buttons in May
= 15 u + 5 u
= 20 u

Total buttons in April : Total buttons in May
46 : 20 _(÷2)
23 : 10 

Answer(s): (a) 18 : 5; (b) 23 : 10