Sean 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 4 : 9. After $104 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 6 : 7. How many of each type did Sean have in the end?

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

	Value of 50-cent	Value of $5	Difference in  value
Before	4x1 = 4 u	9x1 = 9 u	5x1 = 5 u
Change	+ 104	+ 104
After	6x5 = 30 u	7x5 = 35 u	1x5 =  5 u

(a)
The difference in values between 50-cent and $5 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
= 30 u - 4 u
= 26 u

26 u = 104

1 u = 104 ÷ 26 = 4

Value of 50-cent coins in the end
= 30 u
= 30 x 4
= $120

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 120 ÷ 0.50
= 240

(b)
Value of $5 notes in the end
= 35 u
= 35 x 4
= $140

Number of $5 notes in the end
= 140 ÷ 5
= 28

Answer(s): (a) 240; (b) 28