Charlie saved some 50-cent coins and $2 notes in his coin box. The total value of the 50-cent coins to the total value of the $2 notes he had was in the ratio 3 : 11. After $88 worth of 50-cent coins and an equal value of $2 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $2 notes became 5 : 11. How many of each type did Charlie have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
3x3 = 9 u |
11x3 = 33 u |
8x3 = 24 u |
Change |
+ 88 |
+ 88 |
|
After |
5x4 = 20 u |
11x4 = 44 u |
6x4 = 24 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 8 and 6 is 24.
Increase in the value of 50-cent coins after more were added
= 20 u - 9 u
= 11 u
11 u = 88
1 u = 88 ÷ 11 = 8
Value of 50-cent coins in the end
= 20 u
= 20 x 8
= $160
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 160 ÷ 0.50
= 320
(b)
Value of $2 notes in the end
= 44 u
= 44 x 8
= $352
Number of $2 notes in the end
= 352 ÷ 2
= 176
Answer(s): (a) 320; (b) 176