Daniel saved some 20-cent coins and $2 notes in his coin box. The total value of the 20-cent coins to the total value of the $2 notes he had was in the ratio 1 : 6. After $24 worth of 20-cent coins and an equal value of $2 notes were added to the coin box, the ratio of the total value of 20-cent coins to the total value of $2 notes became 1 : 2. How many of each type did Daniel have in the end?
- 20-cent coins?
- $2 notes?
|
Value of 20-cent |
Value of $2 |
Difference in value |
Before |
1x1 = 1 u |
6x1 = 6 u |
5x1 = 5 u |
Change |
+ 24 |
+ 24 |
|
After |
1x5 = 5 u |
2x5 = 10 u |
1x5 = 5 u |
(a)
The difference in values between 20-cent and $2 remains unchanged. Make the difference in value the same. LCM of 5 and 1 is 5.
Increase in the value of 20-cent coins after more were added
= 5 u - 1 u
= 4 u
4 u = 24
1 u = 24 ÷ 4 = 6
Value of 20-cent coins in the end
= 5 u
= 5 x 6
= $30
100¢ = $1
20¢ = $0.20
Number of 20-cent coins in the end
= 30 ÷ 0.20
= 150
(b)
Value of $2 notes in the end
= 10 u
= 10 x 6
= $60
Number of $2 notes in the end
= 60 ÷ 2
= 30
Answer(s): (a) 150; (b) 30