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 5 : 9. After $63 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 7 : 9. 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 |
5x1 = 5 u |
9x1 = 9 u |
4x1 = 4 u |
Change |
+ 63 |
+ 63 |
|
After |
7x2 = 14 u |
9x2 = 18 u |
2x2 = 4 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 4 and 2 is 4.
Increase in the value of 50-cent coins after more were added
= 14 u - 5 u
= 9 u
9 u = 63
1 u = 63 ÷ 9 = 7
Value of 50-cent coins in the end
= 14 u
= 14 x 7
= $98
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 98 ÷ 0.50
= 196
(b)
Value of $1 notes in the end
= 18 u
= 18 x 7
= $126
Number of $1 notes in the end
= 126 ÷ 1
= 126
Answer(s): (a) 196; (b) 126