Julian 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 : 4. After $80 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 Julian have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
1x7 = 7 u |
4x7 = 28 u |
3x7 = 21 u |
Change |
+ 80 |
+ 80 |
|
After |
5x3 = 15 u |
12x3 = 36 u |
7x3 = 21 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 3 and 7 is 21.
Increase in the value of 50-cent coins after more were added
= 15 u - 7 u
= 8 u
8 u = 80
1 u = 80 ÷ 8 = 10
Value of 50-cent coins in the end
= 15 u
= 15 x 10
= $150
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 150 ÷ 0.50
= 300
(b)
Value of $1 notes in the end
= 36 u
= 36 x 10
= $360
Number of $1 notes in the end
= 360 ÷ 1
= 360
Answer(s): (a) 300; (b) 360