Jeremy 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 : 2. After $45 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 8 : 11. How many of each type did Jeremy have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
1x3 = 3 u |
2x3 = 6 u |
1x3 = 3 u |
Change |
+ 45 |
+ 45 |
|
After |
8x1 = 8 u |
11x1 = 11 u |
3x1 = 3 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 1 and 3 is 3.
Increase in the value of 50-cent coins after more were added
= 8 u - 3 u
= 5 u
5 u = 45
1 u = 45 ÷ 5 = 9
Value of 50-cent coins in the end
= 8 u
= 8 x 9
= $72
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 72 ÷ 0.50
= 144
(b)
Value of $1 notes in the end
= 11 u
= 11 x 9
= $99
Number of $1 notes in the end
= 99 ÷ 1
= 99
Answer(s): (a) 144; (b) 99