Paul saved some 50-cent coins and $1 notes in his coin box. The total value of the 50-cent coins to the total value of the $1 notes he had was in the ratio 1 : 4. After $119 worth of 50-cent coins and an equal value of $1 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $1 notes became 7 : 11. How many of each type did Paul have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
1x4 = 4 u |
4x4 = 16 u |
3x4 = 12 u |
Change |
+ 119 |
+ 119 |
|
After |
7x3 = 21 u |
11x3 = 33 u |
4x3 = 12 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 3 and 4 is 12.
Increase in the value of 50-cent coins after more were added
= 21 u - 4 u
= 17 u
17 u = 119
1 u = 119 ÷ 17 = 7
Value of 50-cent coins in the end
= 21 u
= 21 x 7
= $147
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 147 ÷ 0.50
= 294
(b)
Value of $1 notes in the end
= 33 u
= 33 x 7
= $231
Number of $1 notes in the end
= 231 ÷ 1
= 231
Answer(s): (a) 294; (b) 231