Peter saved some 50-cent coins and $5 notes in his coin box. The total value of the 50-cent coins to the total value of the $5 notes he had was in the ratio 2 : 5. After $100 worth of 50-cent coins and an equal value of $5 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $5 notes became 9 : 10. How many of each type did Peter have in the end?
- 50-cent coins?
- $5 notes?
|
Value of 50-cent |
Value of $5 |
Difference in value |
Before |
2x1 = 2 u |
5x1 = 5 u |
3x1 = 3 u |
Change |
+ 100 |
+ 100 |
|
After |
9x3 = 27 u |
10x3 = 30 u |
1x3 = 3 u |
(a)
The difference in values between 50-cent and $5 remains unchanged. Make the difference in value the same. LCM of 3 and 1 is 3.
Increase in the value of 50-cent coins after more were added
= 27 u - 2 u
= 25 u
25 u = 100
1 u = 100 ÷ 25 = 4
Value of 50-cent coins in the end
= 27 u
= 27 x 4
= $108
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 108 ÷ 0.50
= 216
(b)
Value of $5 notes in the end
= 30 u
= 30 x 4
= $120
Number of $5 notes in the end
= 120 ÷ 5
= 24
Answer(s): (a) 216; (b) 24