Simon saved some 50-cent coins and $1 notes in his coin box. The total value of the 50-cent coins to the total value of the $1 notes he had was in the ratio 4 : 9. After $54 worth of 50-cent coins and an equal value of $1 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $1 notes became 2 : 3. How many of each type did Simon have in the end?

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

	Value of 50-cent	Value of $1	Difference in  value
Before	4x1 = 4 u	9x1 = 9 u	5x1 = 5 u
Change	+ 54	+ 54
After	2x5 = 10 u	3x5 = 15 u	1x5 =  5 u

(a)
The difference in values between 50-cent and $1 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 - 4 u
= 6 u

6 u = 54

1 u = 54 ÷ 6 = 9

Value of 50-cent coins in the end
= 10 u
= 10 x 9
= $90

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 90 ÷ 0.50
= 180

(b)
Value of $1 notes in the end
= 15 u
= 15 x 9
= $135

Number of $1 notes in the end
= 135 ÷ 1
= 135

Answer(s): (a) 180; (b) 135