Andy 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 : 13. 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 : 5. How many of each type did Andy have in the end?

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

	Value of 50-cent	Value of $2	Difference in  value
Before	2x3 = 6 u	13x3 = 39 u	11x3 = 33 u
Change	+ 64	+ 64
After	2x11 = 22 u	5x11 = 55 u	3x11 =  33 u

(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 11 and 3 is 33.

Increase in the value of 50-cent coins after more were added
= 22 u - 6 u
= 16 u

16 u = 64

1 u = 64 ÷ 16 = 4

Value of 50-cent coins in the end
= 22 u
= 22 x 4
= $88

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 88 ÷ 0.50
= 176

(b)
Value of $2 notes in the end
= 55 u
= 55 x 4
= $220

Number of $2 notes in the end
= 220 ÷ 2
= 110

Answer(s): (a) 176; (b) 110