Zane 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 : 3. After $30 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 : 9. How many of each type did Zane have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
2x2 = 4 u |
3x2 = 6 u |
1x2 = 2 u |
Change |
+ 30 |
+ 30 |
|
After |
7x1 = 7 u |
9x1 = 9 u |
2x1 = 2 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 1 and 2 is 2.
Increase in the value of 50-cent coins after more were added
= 7 u - 4 u
= 3 u
3 u = 30
1 u = 30 ÷ 3 = 10
Value of 50-cent coins in the end
= 7 u
= 7 x 10
= $70
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 70 ÷ 0.50
= 140
(b)
Value of $2 notes in the end
= 9 u
= 9 x 10
= $90
Number of $2 notes in the end
= 90 ÷ 2
= 45
Answer(s): (a) 140; (b) 45