Xavier 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 4 : 7. After $110 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 Xavier have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
4x1 = 4 u |
7x1 = 7 u |
3x1 = 3 u |
Change |
+ 110 |
+ 110 |
|
After |
5x3 = 15 u |
6x3 = 18 u |
1x3 = 3 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 3 and 1 is 3.
Increase in the value of 50-cent coins after more were added
= 15 u - 4 u
= 11 u
11 u = 110
1 u = 110 ÷ 11 = 10
Value of 50-cent coins in the end
= 15 u
= 15 x 10
= $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
= 18 u
= 18 x 10
= $180
Number of $2 notes in the end
= 180 ÷ 2
= 90
Answer(s): (a) 300; (b) 90