Eric 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 : 13. After $64 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 2 : 9. How many of each type did Eric have in the end?
- 50-cent coins?
- $2 notes?
|
Value of 50-cent |
Value of $2 |
Difference in value |
Before |
2x7 = 14 u |
13x7 = 91 u |
11x7 = 77 u |
Change |
+ 64 |
+ 64 |
|
After |
2x11 = 22 u |
9x11 = 99 u |
7x11 = 77 u |
(a)
The difference in values between 50-cent and $2 remains unchanged. Make the difference in value the same. LCM of 11 and 7 is 77.
Increase in the value of 50-cent coins after more were added
= 22 u - 14 u
= 8 u
8 u = 64
1 u = 64 ÷ 8 = 8
Value of 50-cent coins in the end
= 22 u
= 22 x 8
= $176
100¢ = $1
50¢ = $0.50
Number of 50-cent coins in the end
= 176 ÷ 0.50
= 352
(b)
Value of $2 notes in the end
= 99 u
= 99 x 8
= $792
Number of $2 notes in the end
= 792 ÷ 2
= 396
Answer(s): (a) 352; (b) 396