Jack 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 5 : 13. After $35 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 : 5. How many of each type did Jack have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
5x1 = 5 u |
13x1 = 13 u |
8x1 = 8 u |
Change |
+ 35 |
+ 35 |
|
After |
3x4 = 12 u |
5x4 = 20 u |
2x4 = 8 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 8 and 2 is 8.
Increase in the value of 50-cent coins after more were added
= 12 u - 5 u
= 7 u
7 u = 35
1 u = 35 ÷ 7 = 5
Value of 50-cent coins in the end
= 12 u
= 12 x 5
= $60
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 60 ÷ 0.50
= 120
(b)
Value of $2 notes in the end
= 20 u
= 20 x 5
= $100
Number of $2 notes in the end
= 100 ÷ 2
= 50
Answer(s): (a) 120; (b) 50