Harry saved some 10-cent coins and $2 notes in his coin box. The total value of the 10-cent coins to the total value of the $2 notes he had was in the ratio 1 : 3. After $16 worth of 10-cent coins and an equal value of $2 notes were added to the coin box, the ratio of the total value of 10-cent coins to the total value of $2 notes became 5 : 11. How many of each type did Harry have in the end?
- 10-cent coins?
- $2 notes?
|
Value of 10-cent |
Value of $2 |
Difference in value |
Before |
1x3 = 3 u |
3x3 = 9 u |
2x3 = 6 u |
Change |
+ 16 |
+ 16 |
|
After |
5x1 = 5 u |
11x1 = 11 u |
6x1 = 6 u |
(a)
The difference in values between 10-cent and $2 remains unchanged. Make the difference in value the same. LCM of 2 and 6 is 6.
Increase in the value of 10-cent coins after more were added
= 5 u - 3 u
= 2 u
2 u = 16
1 u = 16 ÷ 2 = 8
Value of 10-cent coins in the end
= 5 u
= 5 x 8
= $40
100¢ = $1
10¢ = $0.10
Number of 10-cent coins in the end
= 40 ÷ 0.10
= 400
(b)
Value of $2 notes in the end
= 11 u
= 11 x 8
= $88
Number of $2 notes in the end
= 88 ÷ 2
= 44
Answer(s): (a) 400; (b) 44