Simon 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 5 : 7. After $77 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 6 : 7. How many of each type did Simon have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
5x1 = 5 u |
7x1 = 7 u |
2x1 = 2 u |
Change |
+ 77 |
+ 77 |
|
After |
6x2 = 12 u |
7x2 = 14 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
= 12 u - 5 u
= 7 u
7 u = 77
1 u = 77 ÷ 7 = 11
Value of 50-cent coins in the end
= 12 u
= 12 x 11
= $132
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 132 ÷ 0.50
= 264
(b)
Value of $1 notes in the end
= 14 u
= 14 x 11
= $154
Number of $1 notes in the end
= 154 ÷ 1
= 154
Answer(s): (a) 264; (b) 154