Will saved some 20-cent coins and $10 notes in his coin box. The total value of the 20-cent coins to the total value of the $10 notes he had was in the ratio 1 : 6. After $52 worth of 20-cent coins and an equal value of $10 notes were added to the coin box, the ratio of the total value of 20-cent coins to the total value of $10 notes became 4 : 11. How many of each type did Will have in the end?
- 20-cent coins?
- $10 notes?
|
Value of 20-cent |
Value of $10 |
Difference in value |
Before |
1x7 = 7 u |
6x7 = 42 u |
5x7 = 35 u |
Change |
+ 52 |
+ 52 |
|
After |
4x5 = 20 u |
11x5 = 55 u |
7x5 = 35 u |
(a)
The difference in values between 20-cent and $10 remains unchanged. Make the difference in value the same. LCM of 5 and 7 is 35.
Increase in the value of 20-cent coins after more were added
= 20 u - 7 u
= 13 u
13 u = 52
1 u = 52 ÷ 13 = 4
Value of 20-cent coins in the end
= 20 u
= 20 x 4
= $80
100¢ = $1
20¢ = $0.20
Number of 20-cent coins in the end
= 80 ÷ 0.20
= 400
(b)
Value of $10 notes in the end
= 55 u
= 55 x 4
= $220
Number of $10 notes in the end
= 220 ÷ 10
= 22
Answer(s): (a) 400; (b) 22