The number of fifty-cent coins in a box was 100% 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
813 less than the number of 20-cent coins. How much money is there in the box?
|
Fifty-cent (1) |
Twenty-cent (2) |
Make u the same (2)x2 = (3) |
Before |
2 u |
1 u |
2 u |
Change |
- 14 |
+ 35 |
+ 70 |
After |
5 p |
13 p |
26 p |
100 + 100100=
200100 =
21 At first
Fifty-cent coins : Twenty-cent coins
2 : 1
1 -
813 =
513 In the end
Fifty-cent coins : Twenty-cent coins
5 : 13
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.
2 u - 14 = 5 p
2 u = 5 p + 14 --- (1)
1 u + 35 = 13 p --- (2)
(2)x2
2 u + 70 = 26 p
2 u = 26 p - 70 --- (3)
(3) = (1)
26 p - 70 = 5 p + 14
26 p - 5 p = 14 + 70
21 p = 84
1 p = 84 ÷ 21 = 4
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 5 p x 50
= 5 x 4 x 50
= 1000¢
Total value of twenty-cent coins in the end
= 13 p x 20
= 13 x 4 x 20
= 1040¢
Total value of the coins
= 1000 + 1040
= 2040¢
= $20.40
Answer(s): $20.40