Tom 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 : 7. After $40 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 7 : 11. How many of each type did Tom have in the end?

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

	Value of 50-cent	Value of $1	Difference in  value
Before	4x4 = 16 u	7x4 = 28 u	3x4 = 12 u
Change	+ 40	+ 40
After	7x3 = 21 u	11x3 = 33 u	4x3 =  12 u

(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 3 and 4 is 12.

Increase in the value of 50-cent coins after more were added
= 21 u - 16 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

Value of 50-cent coins in the end
= 21 u
= 21 x 8
= $168

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 168 ÷ 0.50
= 336

(b)
Value of $1 notes in the end
= 33 u
= 33 x 8
= $264

Number of $1 notes in the end
= 264 ÷ 1
= 264

Answer(s): (a) 336; (b) 264