Xavier 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 : 3. After $152 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 10 : 11. How many of each type did Xavier have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
1x1 = 1 u |
3x1 = 3 u |
2x1 = 2 u |
Change |
+ 152 |
+ 152 |
|
After |
10x2 = 20 u |
11x2 = 22 u |
1x2 = 2 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 2 and 1 is 2.
Increase in the value of 50-cent coins after more were added
= 20 u - 1 u
= 19 u
19 u = 152
1 u = 152 ÷ 19 = 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 $1 notes in the end
= 22 u
= 22 x 8
= $176
Number of $1 notes in the end
= 176 ÷ 1
= 176
Answer(s): (a) 320; (b) 176