Owen 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 1 : 3. After $10 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 5 : 11. How many of each type did Owen have in the end?

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

	Value of 50-cent	Value of $1	Difference in  value
Before	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u
Change	+ 10	+ 10
After	5x1 = 5 u	11x1 = 11 u	6x1 =  6 u

(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 2 and 6 is 6.

Increase in the value of 50-cent coins after more were added
= 5 u - 3 u
= 2 u

2 u = 10

1 u = 10 ÷ 2 = 5

Value of 50-cent coins in the end
= 5 u
= 5 x 5
= $25

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 25 ÷ 0.50
= 50

(b)
Value of $1 notes in the end
= 11 u
= 11 x 5
= $55

Number of $1 notes in the end
= 55 ÷ 1
= 55

Answer(s): (a) 50; (b) 55