In February, Penelope and Luke had coins in the ratio 5 : 3. In March, each of them gave away the same number of coins. Penelope then had five times as many coins as Luke.

1. Find the ratio of the number of coins Luke had in February to the number of coins he had in March.
2. Find the ratio of the total number of coins both had in February to the total number of coins both had in March.

	Penelope	Luke	Difference
Before	5x2 = 10 u	3x2 = 6 u	2x2 = 4 u
Change	- 5 u	- 5 u
After	5x1 = 5 u	1x1 = 1 u	4x1 = 4 u

(a)
Since Penelope and Luke gave away the same number of coins, the difference in the number of coins between Penelope and Luke at first and in the end remains the same.

Make the difference in the number of coins at first and in the end the same. LCM of 2 and 4 is 4.

Luke's coins in February : Luke's coins in March
6 : 1

(b)
Total number of coins in February
= 10 u + 6 u
= 16 u

Total number of coins in March
= 5 u + 1 u
= 6 u

Total coins in February : Total coins in March
16 : 6 _(÷2)
8 : 3 

Answer(s): (a) 6 : 1; (b) 8 : 3