Flynn 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 5 : 8. After $56 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 4 : 5. How many of each type did Flynn have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
5x1 = 5 u |
8x1 = 8 u |
3x1 = 3 u |
Change |
+ 56 |
+ 56 |
|
After |
4x3 = 12 u |
5x3 = 15 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
= 12 u - 5 u
= 7 u
7 u = 56
1 u = 56 ÷ 7 = 8
Value of 50-cent coins in the end
= 12 u
= 12 x 8
= $96
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 96 ÷ 0.50
= 192
(b)
Value of $1 notes in the end
= 15 u
= 15 x 8
= $120
Number of $1 notes in the end
= 120 ÷ 1
= 120
Answer(s): (a) 192; (b) 120