Liam 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 2 : 7. After $42 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 4 : 11. How many of each type did Liam have in the end?

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

	Value of 50-cent	Value of $5	Difference in  value
Before	2x7 = 14 u	7x7 = 49 u	5x7 = 35 u
Change	+ 42	+ 42
After	4x5 = 20 u	11x5 = 55 u	7x5 =  35 u

(a)
The difference in values between 50-cent and $5 remains unchanged. Make the difference in value the same. LCM of 5 and 7 is 35.

Increase in the value of 50-cent coins after more were added
= 20 u - 14 u
= 6 u

6 u = 42

1 u = 42 ÷ 6 = 7

Value of 50-cent coins in the end
= 20 u
= 20 x 7
= $140

100¢ = $1
50¢ = $0.50 

Number of 50-cent coins in the end
= 140 ÷ 0.50
= 280

(b)
Value of $5 notes in the end
= 55 u
= 55 x 7
= $385

Number of $5 notes in the end
= 385 ÷ 5
= 77

Answer(s): (a) 280; (b) 77