Luke saved some 50-cent coins and $1 notes in his coin box. The total value of the 50-cent coins to the total value of the $1 notes he had was in the ratio 1 : 3. After $12 worth of 50-cent coins and an equal value of $1 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $1 notes became 5 : 12. How many of each type did Luke have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
1x7 = 7 u |
3x7 = 21 u |
2x7 = 14 u |
Change |
+ 12 |
+ 12 |
|
After |
5x2 = 10 u |
12x2 = 24 u |
7x2 = 14 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 2 and 7 is 14.
Increase in the value of 50-cent coins after more were added
= 10 u - 7 u
= 3 u
3 u = 12
1 u = 12 ÷ 3 = 4
Value of 50-cent coins in the end
= 10 u
= 10 x 4
= $40
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 40 ÷ 0.50
= 80
(b)
Value of $1 notes in the end
= 24 u
= 24 x 4
= $96
Number of $1 notes in the end
= 96 ÷ 1
= 96
Answer(s): (a) 80; (b) 96