Nick saved some 50-cent coins and $2 notes in his coin box. The total value of the 50-cent coins to the total value of the $2 notes he had was in the ratio 3 : 13. After $63 worth of 50-cent coins and an equal value of $2 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $2 notes became 6 : 11. How many of each type did Nick have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
3x1 = 3 u |
13x1 = 13 u |
10x1 = 10 u |
Change |
+ 63 |
+ 63 |
|
After |
6x2 = 12 u |
11x2 = 22 u |
5x2 = 10 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 10 and 5 is 10.
Increase in the value of 50-cent coins after more were added
= 12 u - 3 u
= 9 u
9 u = 63
1 u = 63 ÷ 9 = 7
Value of 50-cent coins in the end
= 12 u
= 12 x 7
= $84
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 84 ÷ 0.50
= 168
(b)
Value of $2 notes in the end
= 22 u
= 22 x 7
= $154
Number of $2 notes in the end
= 154 ÷ 2
= 77
Answer(s): (a) 168; (b) 77