Fabian 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 3 : 10. After $81 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 3 : 7. How many of each type did Fabian have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
3x4 = 12 u |
10x4 = 40 u |
7x4 = 28 u |
Change |
+ 81 |
+ 81 |
|
After |
3x7 = 21 u |
7x7 = 49 u |
4x7 = 28 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 7 and 4 is 28.
Increase in the value of 50-cent coins after more were added
= 21 u - 12 u
= 9 u
9 u = 81
1 u = 81 ÷ 9 = 9
Value of 50-cent coins in the end
= 21 u
= 21 x 9
= $189
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 189 ÷ 0.50
= 378
(b)
Value of $1 notes in the end
= 49 u
= 49 x 9
= $441
Number of $1 notes in the end
= 441 ÷ 1
= 441
Answer(s): (a) 378; (b) 441