Daniel saved some 10-cent coins and $5 notes in his coin box. The total value of the 10-cent coins to the total value of the $5 notes he had was in the ratio 1 : 3. After $25 worth of 10-cent coins and an equal value of $5 notes were added to the coin box, the ratio of the total value of 10-cent coins to the total value of $5 notes became 7 : 11. How many of each type did Daniel have in the end?
- 10-cent coins?
- $5 notes?
|
Value of 10-cent |
Value of $5 |
Difference in value |
Before |
1x2 = 2 u |
3x2 = 6 u |
2x2 = 4 u |
Change |
+ 25 |
+ 25 |
|
After |
7x1 = 7 u |
11x1 = 11 u |
4x1 = 4 u |
(a)
The difference in values between 10-cent and $5 remains unchanged. Make the difference in value the same. LCM of 2 and 4 is 4.
Increase in the value of 10-cent coins after more were added
= 7 u - 2 u
= 5 u
5 u = 25
1 u = 25 ÷ 5 = 5
Value of 10-cent coins in the end
= 7 u
= 7 x 5
= $35
100¢ = $1
10¢ = $0.10
Number of 10-cent coins in the end
= 35 ÷ 0.10
= 350
(b)
Value of $5 notes in the end
= 11 u
= 11 x 5
= $55
Number of $5 notes in the end
= 55 ÷ 5
= 11
Answer(s): (a) 350; (b) 11