Luis saved some 50-cent coins and $10 notes in his coin box. The total value of the 50-cent coins to the total value of the $10 notes he had was in the ratio 2 : 7. After $52 worth of 50-cent coins and an equal value of $10 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $10 notes became 3 : 4. How many of each type did Luis have in the end?
- 50-cent coins?
- $10 notes?
|
Value of 50-cent |
Value of $10 |
Difference in value |
Before |
2x1 = 2 u |
7x1 = 7 u |
5x1 = 5 u |
Change |
+ 52 |
+ 52 |
|
After |
3x5 = 15 u |
4x5 = 20 u |
1x5 = 5 u |
(a)
The difference in values between 50-cent and $10 remains unchanged. Make the difference in value the same. LCM of 5 and 1 is 5.
Increase in the value of 50-cent coins after more were added
= 15 u - 2 u
= 13 u
13 u = 52
1 u = 52 ÷ 13 = 4
Value of 50-cent coins in the end
= 15 u
= 15 x 4
= $60
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 60 ÷ 0.50
= 120
(b)
Value of $10 notes in the end
= 20 u
= 20 x 4
= $80
Number of $10 notes in the end
= 80 ÷ 10
= 8
Answer(s): (a) 120; (b) 8