Reggie saved some 20-cent coins and $1 notes in his coin box. The total value of the 20-cent coins to the total value of the $1 notes he had was in the ratio 1 : 4. After $8 worth of 20-cent coins and an equal value of $1 notes were added to the coin box, the ratio of the total value of 20-cent coins to the total value of $1 notes became 1 : 2. How many of each type did Reggie have in the end?
- 20-cent coins?
- $1 notes?
|
Value of 20-cent |
Value of $1 |
Difference in value |
Before |
1x1 = 1 u |
4x1 = 4 u |
3x1 = 3 u |
Change |
+ 8 |
+ 8 |
|
After |
1x3 = 3 u |
2x3 = 6 u |
1x3 = 3 u |
(a)
The difference in values between 20-cent and $1 remains unchanged. Make the difference in value the same. LCM of 3 and 1 is 3.
Increase in the value of 20-cent coins after more were added
= 3 u - 1 u
= 2 u
2 u = 8
1 u = 8 ÷ 2 = 4
Value of 20-cent coins in the end
= 3 u
= 3 x 4
= $12
100¢ = $1
20¢ = $0.20
Number of 20-cent coins in the end
= 12 ÷ 0.20
= 60
(b)
Value of $1 notes in the end
= 6 u
= 6 x 4
= $24
Number of $1 notes in the end
= 24 ÷ 1
= 24
Answer(s): (a) 60; (b) 24