Will 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 : 7. After $21 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 4 : 5. How many of each type did Will have in the end?

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

	Value of 50-cent	Value of $10	Difference in  value
Before	5x1 = 5 u	7x1 = 7 u	2x1 = 2 u
Change	+ 21	+ 21
After	4x2 = 8 u	5x2 = 10 u	1x2 =  2 u

(a)
The difference in values between 50-cent and $10 remains unchanged. Make the difference in value the same. LCM of 2 and 1 is 2.

Increase in the value of 50-cent coins after more were added
= 8 u - 5 u
= 3 u

3 u = 21

1 u = 21 ÷ 3 = 7

Value of 50-cent coins in the end
= 8 u
= 8 x 7
= $56

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 56 ÷ 0.50
= 112

(b)
Value of $10 notes in the end
= 10 u
= 10 x 7
= $70

Number of $10 notes in the end
= 70 ÷ 10
= 7

Answer(s): (a) 112; (b) 7