The number of fifty-cent coins in a bag was 200% more than the number of twenty-cent coins. 14 fifty-cent coins were taken out and exchanged for twenty-cent coins. The number of 50-cent coins became
37 less than the number of 20-cent coins. How much money is there in the bag?
|
Fifty-cent (1) |
Twenty-cent (2) |
Make u the same (2)x3 = (3) |
Before |
3 u |
1 u |
3 u |
Change |
- 14 |
+ 35 |
+ 105 |
After |
4 p |
7 p |
21 p |
100 + 200100=
300100 =
31 At first
Fifty-cent coins : Twenty-cent coins
3 : 1
1 -
37 =
47 In the end
Fifty-cent coins : Twenty-cent coins
4 : 7
Total value of 50-cent coins to be taken out
= 14 x 50
= 700¢
Total number of 20-cent coins to be exchanged for
= 700 ÷ 20
= 35
Notice that the number of 20-cent coins is 1 u at first. So, instead of making p the same, we can make u the same so we create one extra equation instead of 2.
3 u - 14 = 4 p
3 u = 4 p + 14 --- (1)
1 u + 35 = 7 p --- (2)
(2)x3
3 u + 105 = 21 p
3 u = 21 p - 105 --- (3)
(3) = (1)
21 p - 105 = 4 p + 14
21 p - 4 p = 14 + 105
17 p = 119
1 p = 119 ÷ 17 = 7
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 4 p x 50
= 4 x 7 x 50
= 1400¢
Total value of twenty-cent coins in the end
= 7 p x 20
= 7 x 7 x 20
= 980¢
Total value of the coins
= 1400 + 980
= 2380¢
= $23.80
Answer(s): $23.80