Dylan 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 1 : 6. After $130 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 3 : 5. How many of each type did Dylan have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
1x2 = 2 u |
6x2 = 12 u |
5x2 = 10 u |
Change |
+ 130 |
+ 130 |
|
After |
3x5 = 15 u |
5x5 = 25 u |
2x5 = 10 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 5 and 2 is 10.
Increase in the value of 50-cent coins after more were added
= 15 u - 2 u
= 13 u
13 u = 130
1 u = 130 ÷ 13 = 10
Value of 50-cent coins in the end
= 15 u
= 15 x 10
= $150
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 150 ÷ 0.50
= 300
(b)
Value of $1 notes in the end
= 25 u
= 25 x 10
= $250
Number of $1 notes in the end
= 250 ÷ 1
= 250
Answer(s): (a) 300; (b) 250