Simon 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 2 : 13. After $76 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 3 : 10. How many of each type did Simon have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
2x7 = 14 u |
13x7 = 91 u |
11x7 = 77 u |
Change |
+ 76 |
+ 76 |
|
After |
3x11 = 33 u |
10x11 = 110 u |
7x11 = 77 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 11 and 7 is 77.
Increase in the value of 50-cent coins after more were added
= 33 u - 14 u
= 19 u
19 u = 76
1 u = 76 ÷ 19 = 4
Value of 50-cent coins in the end
= 33 u
= 33 x 4
= $132
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 132 ÷ 0.50
= 264
(b)
Value of $2 notes in the end
= 110 u
= 110 x 4
= $440
Number of $2 notes in the end
= 440 ÷ 2
= 220
Answer(s): (a) 264; (b) 220