Bobby 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 2 : 7. After $64 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 2 : 3. How many of each type did Bobby have in the end?

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

	Value of 50-cent	Value of $2	Difference in  value
Before	2x1 = 2 u	7x1 = 7 u	5x1 = 5 u
Change	+ 64	+ 64
After	2x5 = 10 u	3x5 = 15 u	1x5 =  5 u

(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 5 and 1 is 5.

Increase in the value of 50-cent coins after more were added
= 10 u - 2 u
= 8 u

8 u = 64

1 u = 64 ÷ 8 = 8

Value of 50-cent coins in the end
= 10 u
= 10 x 8
= $80

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 80 ÷ 0.50
= 160

(b)
Value of $2 notes in the end
= 15 u
= 15 x 8
= $120

Number of $2 notes in the end
= 120 ÷ 2
= 60

Answer(s): (a) 160; (b) 60