Lee saved some 50-cent coins and $5 notes in his coin box. The total value of the 50-cent coins to the total value of the $5 notes he had was in the ratio 5 : 12. After $161 worth of 50-cent coins and an equal value of $5 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $5 notes became 4 : 5. How many of each type did Lee have in the end?

1. 50-cent coins?
2. $5 notes?

	Value of 50-cent	Value of $5	Difference in  value
Before	5x1 = 5 u	12x1 = 12 u	7x1 = 7 u
Change	+ 161	+ 161
After	4x7 = 28 u	5x7 = 35 u	1x7 =  7 u

(a)
The difference in values between 50-cent and $5 remains unchanged. Make the difference in value the same. LCM of 7 and 1 is 7.

Increase in the value of 50-cent coins after more were added
= 28 u - 5 u
= 23 u

23 u = 161

1 u = 161 ÷ 23 = 7

Value of 50-cent coins in the end
= 28 u
= 28 x 7
= $196

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 196 ÷ 0.50
= 392

(b)
Value of $5 notes in the end
= 35 u
= 35 x 7
= $245

Number of $5 notes in the end
= 245 ÷ 5
= 49

Answer(s): (a) 392; (b) 49