In March, Cathy and Zeph had coins in the ratio 12 : 7. In April, each of them gave away the same number of coins. Cathy then had five times as many coins as Zeph.

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

	Cathy	Zeph	Difference
Before	12x4 = 48 u	7x4 = 28 u	5x4 = 20 u
Change	- 23 u	- 23 u
After	5x5 = 25 u	1x5 = 5 u	4x5 = 20 u

(a)
Since Cathy and Zeph gave away the same number of coins, the difference in the number of coins between Cathy and Zeph 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 5 and 4 is 20.

Zeph's coins in March : Zeph's coins in April
28 : 5

(b)
Total number of coins in March
= 48 u + 28 u
= 76 u

Total number of coins in April
= 25 u + 5 u
= 30 u

Total coins in March : Total coins in April
76 : 30 _(÷2)
38 : 15 

Answer(s): (a) 28 : 5; (b) 38 : 15