Fred saved some 50-cent coins and $1 notes in his coin box. The total value of the 50-cent coins to the total value of the $1 notes he had was in the ratio 1 : 4. After $100 worth of 50-cent coins and an equal value of $1 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $1 notes became 7 : 8. How many of each type did Fred have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
1x1 = 1 u |
4x1 = 4 u |
3x1 = 3 u |
Change |
+ 100 |
+ 100 |
|
After |
7x3 = 21 u |
8x3 = 24 u |
1x3 = 3 u |
(a)
The difference in values between 50-cent and $1 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
= 21 u - 1 u
= 20 u
20 u = 100
1 u = 100 ÷ 20 = 5
Value of 50-cent coins in the end
= 21 u
= 21 x 5
= $105
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 105 ÷ 0.50
= 210
(b)
Value of $1 notes in the end
= 24 u
= 24 x 5
= $120
Number of $1 notes in the end
= 120 ÷ 1
= 120
Answer(s): (a) 210; (b) 120