The number of fifty-cent coins in a box was 200% more than the number of twenty-cent coins. 16 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)x3 = (3) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 16 |
+ 40 |
+ 120 |
| After |
5 p |
13 p |
39 p |
100 + 200100=
300100 =
31 At first
Fifty-cent coins : Twenty-cent coins
3 : 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
= 16 x 50
= 800¢
Total number of 20-cent coins to be exchanged for
= 800 ÷ 20
= 40
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 - 16 = 5 p
3 u = 5 p + 16 --- (1)
1 u + 40 = 13 p --- (2)
(2)x3
3 u + 120 = 39 p
3 u = 39 p - 120 --- (3)
(3) = (1)
39 p - 120 = 5 p + 16
39 p - 5 p = 16 + 120
34 p = 136
1 p = 136 ÷ 34 = 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
