In May, Fiona and John had marbles in the ratio 8 : 3. In June, each of them gave away the same number of marbles. Fiona then had five times as many marbles as John.

1. Find the ratio of the number of marbles John 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.

	Fiona	John	Difference
Before	8x4 = 32 u	3x4 = 12 u	5x4 = 20 u
Change	- 7 u	- 7 u
After	5x5 = 25 u	1x5 = 5 u	4x5 = 20 u

(a)
Since Fiona and John gave away the same number of marbles, the difference in the number of marbles between Fiona and John 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 4 is 20.

John's marbles in May : John's marbles in June
12 : 5

(b)
Total number of marbles in May
= 32 u + 12 u
= 44 u

Total number of marbles in June
= 25 u + 5 u
= 30 u

Total marbles in May : Total marbles in June
44 : 30 _(÷2)
22 : 15 

Answer(s): (a) 12 : 5; (b) 22 : 15