Eric saved some 20-cent coins and $2 notes in his coin box. The total value of the 20-cent coins to the total value of the $2 notes he had was in the ratio 1 : 2. After $30 worth of 20-cent coins and an equal value of $2 notes were added to the coin box, the ratio of the total value of 20-cent coins to the total value of $2 notes became 7 : 11. How many of each type did Eric have in the end?
- 20-cent coins?
- $2 notes?
|
Value of 20-cent |
Value of $2 |
Difference in value |
Before |
1x4 = 4 u |
2x4 = 8 u |
1x4 = 4 u |
Change |
+ 30 |
+ 30 |
|
After |
7x1 = 7 u |
11x1 = 11 u |
4x1 = 4 u |
(a)
The difference in values between 20-cent and $2 remains unchanged. Make the difference in value the same. LCM of 1 and 4 is 4.
Increase in the value of 20-cent coins after more were added
= 7 u - 4 u
= 3 u
3 u = 30
1 u = 30 ÷ 3 = 10
Value of 20-cent coins in the end
= 7 u
= 7 x 10
= $70
100¢ = $1
20¢ = $0.20
Number of 20-cent coins in the end
= 70 ÷ 0.20
= 350
(b)
Value of $2 notes in the end
= 11 u
= 11 x 10
= $110
Number of $2 notes in the end
= 110 ÷ 2
= 55
Answer(s): (a) 350; (b) 55