Jeremy saved some 50-cent coins and $10 notes in his coin box. The total value of the 50-cent coins to the total value of the $10 notes he had was in the ratio 5 : 12. After $44 worth of 50-cent coins and an equal value of $10 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $10 notes became 3 : 5. How many of each type did Jeremy have in the end?

1. 50-cent coins?
2. $10 notes?

	Value of 50-cent	Value of $10	Difference in  value
Before	5x2 = 10 u	12x2 = 24 u	7x2 = 14 u
Change	+ 44	+ 44
After	3x7 = 21 u	5x7 = 35 u	2x7 =  14 u

(a)
The difference in values between 50-cent and $10 remains unchanged. Make the difference in value the same. LCM of 7 and 2 is 14.

Increase in the value of 50-cent coins after more were added
= 21 u - 10 u
= 11 u

11 u = 44

1 u = 44 ÷ 11 = 4

Value of 50-cent coins in the end
= 21 u
= 21 x 4
= $84

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 84 ÷ 0.50
= 168

(b)
Value of $10 notes in the end
= 35 u
= 35 x 4
= $140

Number of $10 notes in the end
= 140 ÷ 10
= 14

Answer(s): (a) 168; (b) 14