Jeremy 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 : 5. After $35 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 2 : 5. How many of each type did Jeremy have in the end?
- 50-cent coins?
- $10 notes?
|
Value of 50-cent |
Value of $10 |
Difference in value |
Before |
1x3 = 3 u |
5x3 = 15 u |
4x3 = 12 u |
Change |
+ 35 |
+ 35 |
|
After |
2x4 = 8 u |
5x4 = 20 u |
3x4 = 12 u |
(a)
The difference in values between 50-cent and $10 remains unchanged. Make the difference in value the same. LCM of 4 and 3 is 12.
Increase in the value of 50-cent coins after more were added
= 8 u - 3 u
= 5 u
5 u = 35
1 u = 35 ÷ 5 = 7
Value of 50-cent coins in the end
= 8 u
= 8 x 7
= $56
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 56 ÷ 0.50
= 112
(b)
Value of $10 notes in the end
= 20 u
= 20 x 7
= $140
Number of $10 notes in the end
= 140 ÷ 10
= 14
Answer(s): (a) 112; (b) 14