Charlie saved some 50-cent coins and $10 notes in his coin box. The total value of the 50-cent coins to the total value of the $10 notes he had was in the ratio 3 : 13. After $36 worth of 50-cent coins and an equal value of $10 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $10 notes became 3 : 7. How many of each type did Charlie have in the end?
- 50-cent coins?
- $10 notes?
|
Value of 50-cent |
Value of $10 |
Difference in value |
Before |
3x2 = 6 u |
13x2 = 26 u |
10x2 = 20 u |
Change |
+ 36 |
+ 36 |
|
After |
3x5 = 15 u |
7x5 = 35 u |
4x5 = 20 u |
(a)
The difference in values between 50-cent and $10 remains unchanged. Make the difference in value the same. LCM of 10 and 4 is 20.
Increase in the value of 50-cent coins after more were added
= 15 u - 6 u
= 9 u
9 u = 36
1 u = 36 ÷ 9 = 4
Value of 50-cent coins in the end
= 15 u
= 15 x 4
= $60
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 60 ÷ 0.50
= 120
(b)
Value of $10 notes in the end
= 35 u
= 35 x 4
= $140
Number of $10 notes in the end
= 140 ÷ 10
= 14
Answer(s): (a) 120; (b) 14