Albert saved some 50-cent coins and $2 notes in his coin box. The total value of the 50-cent coins to the total value of the $2 notes he had was in the ratio 1 : 4. After $28 worth of 50-cent coins and an equal value of $2 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $2 notes became 3 : 8. How many of each type did Albert have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
1x5 = 5 u |
4x5 = 20 u |
3x5 = 15 u |
Change |
+ 28 |
+ 28 |
|
After |
3x3 = 9 u |
8x3 = 24 u |
5x3 = 15 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 3 and 5 is 15.
Increase in the value of 50-cent coins after more were added
= 9 u - 5 u
= 4 u
4 u = 28
1 u = 28 ÷ 4 = 7
Value of 50-cent coins in the end
= 9 u
= 9 x 7
= $63
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 63 ÷ 0.50
= 126
(b)
Value of $2 notes in the end
= 24 u
= 24 x 7
= $168
Number of $2 notes in the end
= 168 ÷ 2
= 84
Answer(s): (a) 126; (b) 84