In May, Tammy and Riordan had marbles in the ratio 14 : 9. In June, each of them gave away the same number of marbles. Tammy then had thrice as many marbles as Riordan.

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

	Tammy	Riordan	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 Tammy and Riordan gave away the same number of marbles, the difference in the number of marbles between Tammy and Riordan at first and in the end remains the same.

Make the difference in the number of marbles at first and in the end the same. LCM of 5 and 2 is 10.

Riordan's marbles in May : Riordan's marbles in June
18 : 5

(b)
Total number of marbles in May
= 28 u + 18 u
= 46 u

Total number of marbles in June
= 15 u + 5 u
= 20 u

Total marbles in May : Total marbles in June
46 : 20 _(÷2)
23 : 10 

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