The number of fifty-cent coins in a box was 100% more than the number of ten-cent coins. 6 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
38 less than the number of 10-cent coins. How much money is there in the box?
| |
Fifty-cent
(1) |
Ten-cent
(2) |
Make u the same
(2)x2 = (3) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 |
+ 30 |
+ 60 |
| After |
5 p |
8 p |
16 p |
100 + 100100=
200100 =
21 At first
Fifty-cent coins : Ten-cent coins
2 : 1
1 -
38 =
58 In the end
Fifty-cent coins : Ten-cent coins
5 : 8
Total value of 50-cent coins to be taken out
= 6 x 50
= 300¢
Total number of 10-cent coins to be exchanged for
= 300 ÷ 10
= 30
Notice that the number of 10-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 - 6 = 5 p
2 u = 5 p + 6 --- (1)
1 u + 30 = 8 p --- (2)
(2)x2
2 u + 60 = 16 p
2 u = 16 p - 60 --- (3)
(3) = (1)
16 p - 60 = 5 p + 6
16 p - 5 p = 6 + 60
11 p = 66
1 p = 66 ÷ 11 = 6
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 6 x 50
= 1500¢
Total value of ten-cent coins in the end
= 8 p x 10
= 8 x 6 x 10
= 480¢
Total value of the coins
= 1500 + 480
= 1980¢
= $19.80
Answer(s): $19.80
