Jenson saved some 50-cent coins and $10 notes in his coin box. The total value of the 50-cent coins to the total value of the $10 notes he had was in the ratio 1 : 3. After $20 worth of 50-cent coins and an equal value of $10 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $10 notes became 5 : 11. How many of each type did Jenson have in the end?
- 50-cent coins?
- $10 notes?
|
Value of 50-cent |
Value of $10 |
Difference in value |
Before |
1x3 = 3 u |
3x3 = 9 u |
2x3 = 6 u |
Change |
+ 20 |
+ 20 |
|
After |
5x1 = 5 u |
11x1 = 11 u |
6x1 = 6 u |
(a)
The difference in values between 50-cent and $10 remains unchanged. Make the difference in value the same. LCM of 2 and 6 is 6.
Increase in the value of 50-cent coins after more were added
= 5 u - 3 u
= 2 u
2 u = 20
1 u = 20 ÷ 2 = 10
Value of 50-cent coins in the end
= 5 u
= 5 x 10
= $50
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 50 ÷ 0.50
= 100
(b)
Value of $10 notes in the end
= 11 u
= 11 x 10
= $110
Number of $10 notes in the end
= 110 ÷ 10
= 11
Answer(s): (a) 100; (b) 11