Justin 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 : 5. After $102 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 5 : 8. How many of each type did Justin have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
1x3 = 3 u |
5x3 = 15 u |
4x3 = 12 u |
Change |
+ 102 |
+ 102 |
|
After |
5x4 = 20 u |
8x4 = 32 u |
3x4 = 12 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 4 and 3 is 12.
Increase in the value of 50-cent coins after more were added
= 20 u - 3 u
= 17 u
17 u = 102
1 u = 102 ÷ 17 = 6
Value of 50-cent coins in the end
= 20 u
= 20 x 6
= $120
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 120 ÷ 0.50
= 240
(b)
Value of $2 notes in the end
= 32 u
= 32 x 6
= $192
Number of $2 notes in the end
= 192 ÷ 2
= 96
Answer(s): (a) 240; (b) 96