Vincent saved some 50-cent coins and $10 notes in his coin box. The total value of the 50-cent coins to the total value of the $10 notes he had was in the ratio 1 : 3. After $30 worth of 50-cent coins and an equal value of $10 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $10 notes became 5 : 12. How many of each type did Vincent have in the end?

1. 50-cent coins?
2. $10 notes?

	Value of 50-cent	Value of $10	Difference in  value
Before	1x7 = 7 u	3x7 = 21 u	2x7 = 14 u
Change	+ 30	+ 30
After	5x2 = 10 u	12x2 = 24 u	7x2 =  14 u

(a)
The difference in values between 50-cent and $10 remains unchanged. Make the difference in value the same. LCM of 2 and 7 is 14.

Increase in the value of 50-cent coins after more were added
= 10 u - 7 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Value of 50-cent coins in the end
= 10 u
= 10 x 10
= $100

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 100 ÷ 0.50
= 200

(b)
Value of $10 notes in the end
= 24 u
= 24 x 10
= $240

Number of $10 notes in the end
= 240 ÷ 10
= 24

Answer(s): (a) 200; (b) 24