In April, Jade and Luke had marbles in the ratio 13 : 9. In May, each of them gave away the same number of marbles. Jade then had twice as many marbles as Luke.

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

	Jade	Luke	Difference
Before	13x1 = 13 u	9x1 = 9 u	4x1 = 4 u
Change	- 5 u	- 5 u
After	2x4 = 8 u	1x4 = 4 u	1x4 = 4 u

(a)
Since Jade and Luke gave away the same number of marbles, the difference in the number of marbles between Jade and Luke 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 4 and 1 is 4.

Luke's marbles in April : Luke's marbles in May
9 : 4

(b)
Total number of marbles in April
= 13 u + 9 u
= 22 u

Total number of marbles in May
= 8 u + 4 u
= 12 u

Total marbles in April : Total marbles in May
22 : 12 _(÷2)
11 : 6 

Answer(s): (a) 9 : 4; (b) 11 : 6