Eric 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 4 : 9. How many of each type did Eric have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
1x5 = 5 u |
3x5 = 15 u |
2x5 = 10 u |
Change |
+ 12 |
+ 12 |
|
After |
4x2 = 8 u |
9x2 = 18 u |
5x2 = 10 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 2 and 5 is 10.
Increase in the value of 50-cent coins after more were added
= 8 u - 5 u
= 3 u
3 u = 12
1 u = 12 ÷ 3 = 4
Value of 50-cent coins in the end
= 8 u
= 8 x 4
= $32
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 32 ÷ 0.50
= 64
(b)
Value of $1 notes in the end
= 18 u
= 18 x 4
= $72
Number of $1 notes in the end
= 72 ÷ 1
= 72
Answer(s): (a) 64; (b) 72