In May, Kathy and Andy had erasers in the ratio 9 : 8. In June, each of them gave away the same number of erasers. Kathy then had thrice as many erasers as Andy.

1. Find the ratio of the number of erasers Andy had in May to the number of erasers he had in June.
2. Find the ratio of the total number of erasers both had in May to the total number of erasers both had in June.

	Kathy	Andy	Difference
Before	9x2 = 18 u	8x2 = 16 u	1x2 = 2 u
Change	- 15 u	- 15 u
After	3x1 = 3 u	1x1 = 1 u	2x1 = 2 u

(a)
Since Kathy and Andy gave away the same number of erasers, the difference in the number of erasers between Kathy and Andy at first and in the end remains the same.

Make the difference in the number of erasers at first and in the end the same. LCM of 1 and 2 is 2.

Andy's erasers in May : Andy's erasers in June
16 : 1

(b)
Total number of erasers in May
= 18 u + 16 u
= 34 u

Total number of erasers in June
= 3 u + 1 u
= 4 u

Total erasers in May : Total erasers in June
34 : 4 _(÷2)
17 : 2 

Answer(s): (a) 16 : 1; (b) 17 : 2