Xavier saved some 20-cent coins and $5 notes in his coin box. The total value of the 20-cent coins to the total value of the $5 notes he had was in the ratio 5 : 11. After $36 worth of 20-cent coins and an equal value of $5 notes were added to the coin box, the ratio of the total value of 20-cent coins to the total value of $5 notes became 7 : 10. How many of each type did Xavier have in the end?
- 20-cent coins?
- $5 notes?
|
Value of 20-cent |
Value of $5 |
Difference in value |
Before |
5x1 = 5 u |
11x1 = 11 u |
6x1 = 6 u |
Change |
+ 36 |
+ 36 |
|
After |
7x2 = 14 u |
10x2 = 20 u |
3x2 = 6 u |
(a)
The difference in values between 20-cent and $5 remains unchanged. Make the difference in value the same. LCM of 6 and 3 is 6.
Increase in the value of 20-cent coins after more were added
= 14 u - 5 u
= 9 u
9 u = 36
1 u = 36 ÷ 9 = 4
Value of 20-cent coins in the end
= 14 u
= 14 x 4
= $56
100¢ = $1
20¢ = $0.20
Number of 20-cent coins in the end
= 56 ÷ 0.20
= 280
(b)
Value of $5 notes in the end
= 20 u
= 20 x 4
= $80
Number of $5 notes in the end
= 80 ÷ 5
= 16
Answer(s): (a) 280; (b) 16