Daniel 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 5 : 7. After $52 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 9 : 10. How many of each type did Daniel have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
5x1 = 5 u |
7x1 = 7 u |
2x1 = 2 u |
Change |
+ 52 |
+ 52 |
|
After |
9x2 = 18 u |
10x2 = 20 u |
1x2 = 2 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 2 and 1 is 2.
Increase in the value of 50-cent coins after more were added
= 18 u - 5 u
= 13 u
13 u = 52
1 u = 52 ÷ 13 = 4
Value of 50-cent coins in the end
= 18 u
= 18 x 4
= $72
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 72 ÷ 0.50
= 144
(b)
Value of $2 notes in the end
= 20 u
= 20 x 4
= $80
Number of $2 notes in the end
= 80 ÷ 2
= 40
Answer(s): (a) 144; (b) 40