Caden 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 : 8. After $132 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 : 6. How many of each type did Caden have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
3x1 = 3 u |
8x1 = 8 u |
5x1 = 5 u |
Change |
+ 132 |
+ 132 |
|
After |
5x5 = 25 u |
6x5 = 30 u |
1x5 = 5 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 5 and 1 is 5.
Increase in the value of 50-cent coins after more were added
= 25 u - 3 u
= 22 u
22 u = 132
1 u = 132 ÷ 22 = 6
Value of 50-cent coins in the end
= 25 u
= 25 x 6
= $150
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 150 ÷ 0.50
= 300
(b)
Value of $2 notes in the end
= 30 u
= 30 x 6
= $180
Number of $2 notes in the end
= 180 ÷ 2
= 90
Answer(s): (a) 300; (b) 90