Pierre saved some 20-cent coins and $1 notes in his coin box. The total value of the 20-cent coins to the total value of the $1 notes he had was in the ratio 3 : 7. After $28 worth of 20-cent coins and an equal value of $1 notes were added to the coin box, the ratio of the total value of 20-cent coins to the total value of $1 notes became 5 : 7. How many of each type did Pierre have in the end?
- 20-cent coins?
- $1 notes?
|
Value of 20-cent |
Value of $1 |
Difference in value |
Before |
3x1 = 3 u |
7x1 = 7 u |
4x1 = 4 u |
Change |
+ 28 |
+ 28 |
|
After |
5x2 = 10 u |
7x2 = 14 u |
2x2 = 4 u |
(a)
The difference in values between 20-cent and $1 remains unchanged. Make the difference in value the same. LCM of 4 and 2 is 4.
Increase in the value of 20-cent coins after more were added
= 10 u - 3 u
= 7 u
7 u = 28
1 u = 28 ÷ 7 = 4
Value of 20-cent coins in the end
= 10 u
= 10 x 4
= $40
100¢ = $1
20¢ = $0.20
Number of 20-cent coins in the end
= 40 ÷ 0.20
= 200
(b)
Value of $1 notes in the end
= 14 u
= 14 x 4
= $56
Number of $1 notes in the end
= 56 ÷ 1
= 56
Answer(s): (a) 200; (b) 56