Simon saved some 50-cent coins and $5 notes in his coin box. The total value of the 50-cent coins to the total value of the $5 notes he had was in the ratio 1 : 3. After $150 worth of 50-cent coins and an equal value of $5 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $5 notes became 8 : 9. How many of each type did Simon have in the end?
- 50-cent coins?
- $5 notes?
|
Value of 50-cent |
Value of $5 |
Difference in value |
Before |
1x1 = 1 u |
3x1 = 3 u |
2x1 = 2 u |
Change |
+ 150 |
+ 150 |
|
After |
8x2 = 16 u |
9x2 = 18 u |
1x2 = 2 u |
(a)
The difference in values between 50-cent and $5 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
= 16 u - 1 u
= 15 u
15 u = 150
1 u = 150 ÷ 15 = 10
Value of 50-cent coins in the end
= 16 u
= 16 x 10
= $160
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 160 ÷ 0.50
= 320
(b)
Value of $5 notes in the end
= 18 u
= 18 x 10
= $180
Number of $5 notes in the end
= 180 ÷ 5
= 36
Answer(s): (a) 320; (b) 36