In May, Linda and Flynn had marbles in the ratio 7 : 4. In June, each of them gave away the same number of marbles. Linda then had five times as many marbles as Flynn.

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

	Linda	Flynn	Difference
Before	7x4 = 28 u	4x4 = 16 u	3x4 = 12 u
Change	- 13 u	- 13 u
After	5x3 = 15 u	1x3 = 3 u	4x3 = 12 u

(a)
Since Linda and Flynn gave away the same number of marbles, the difference in the number of marbles between Linda and Flynn 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 3 and 4 is 12.

Flynn's marbles in May : Flynn's marbles in June
16 : 3

(b)
Total number of marbles in May
= 28 u + 16 u
= 44 u

Total number of marbles in June
= 15 u + 3 u
= 18 u

Total marbles in May : Total marbles in June
44 : 18 _(÷2)
22 : 9 

Answer(s): (a) 16 : 3; (b) 22 : 9