Vincent saved some 50-cent coins and $2 notes in his coin box. The total value of the 50-cent coins to the total value of the $2 notes he had was in the ratio 1 : 3. After $117 worth of 50-cent coins and an equal value of $2 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $2 notes became 7 : 8. How many of each type did Vincent have in the end?

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

	Value of 50-cent	Value of $2	Difference in  value
Before	1x1 = 1 u	3x1 = 3 u	2x1 = 2 u
Change	+ 117	+ 117
After	7x2 = 14 u	8x2 = 16 u	1x2 =  2 u

(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 2 and 1 is 2.

Increase in the value of 50-cent coins after more were added
= 14 u - 1 u
= 13 u

13 u = 117

1 u = 117 ÷ 13 = 9

Value of 50-cent coins in the end
= 14 u
= 14 x 9
= $126

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 126 ÷ 0.50
= 252

(b)
Value of $2 notes in the end
= 16 u
= 16 x 9
= $144

Number of $2 notes in the end
= 144 ÷ 2
= 72

Answer(s): (a) 252; (b) 72