Ethan saved some 20-cent coins and $5 notes in his coin box. The total value of the 20-cent coins to the total value of the $5 notes he had was in the ratio 5 : 13. After $42 worth of 20-cent coins and an equal value of $5 notes were added to the coin box, the ratio of the total value of 20-cent coins to the total value of $5 notes became 3 : 5. How many of each type did Ethan have in the end?

1. 20-cent coins?
2. $5 notes?

	Value of 20-cent	Value of $5	Difference in  value
Before	5x1 = 5 u	13x1 = 13 u	8x1 = 8 u
Change	+ 42	+ 42
After	3x4 = 12 u	5x4 = 20 u	2x4 =  8 u

(a)
The difference in values between 20-cent and $5 remains unchanged. Make the difference in value the same. LCM of 8 and 2 is 8.

Increase in the value of 20-cent coins after more were added
= 12 u - 5 u
= 7 u

7 u = 42

1 u = 42 ÷ 7 = 6

Value of 20-cent coins in the end
= 12 u
= 12 x 6
= $72

100¢ = $1
20¢ = $0.20 

Number of 20-cent coins in the end
= 72 ÷ 0.20
= 360

(b)
Value of $5 notes in the end
= 20 u
= 20 x 6
= $120

Number of $5 notes in the end
= 120 ÷ 5
= 24

Answer(s): (a) 360; (b) 24