Japheth 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 : 4. After $42 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 4 : 9. How many of each type did Japheth have in the end?
- 50-cent coins?
- $1 notes?
|
Value of 50-cent |
Value of $1 |
Difference in value |
Before |
1x5 = 5 u |
4x5 = 20 u |
3x5 = 15 u |
Change |
+ 42 |
+ 42 |
|
After |
4x3 = 12 u |
9x3 = 27 u |
5x3 = 15 u |
(a)
The difference in values between 50-cent and $1 remains unchanged. Make the difference in value the same. LCM of 3 and 5 is 15.
Increase in the value of 50-cent coins after more were added
= 12 u - 5 u
= 7 u
7 u = 42
1 u = 42 ÷ 7 = 6
Value of 50-cent coins in the end
= 12 u
= 12 x 6
= $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
= 27 u
= 27 x 6
= $162
Number of $1 notes in the end
= 162 ÷ 1
= 162
Answer(s): (a) 144; (b) 162