Vaidev 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 : 11. After $133 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 7 : 10. How many of each type did Vaidev have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
2x1 = 2 u |
11x1 = 11 u |
9x1 = 9 u |
Change |
+ 133 |
+ 133 |
|
After |
7x3 = 21 u |
10x3 = 30 u |
3x3 = 9 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 9 and 3 is 9.
Increase in the value of 50-cent coins after more were added
= 21 u - 2 u
= 19 u
19 u = 133
1 u = 133 ÷ 19 = 7
Value of 50-cent coins in the end
= 21 u
= 21 x 7
= $147
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 147 ÷ 0.50
= 294
(b)
Value of $2 notes in the end
= 30 u
= 30 x 7
= $210
Number of $2 notes in the end
= 210 ÷ 2
= 105
Answer(s): (a) 294; (b) 105