The number of fifty-cent coins in a basket was 300% more than the number of ten-cent coins. 13 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
611 less than the number of 10-cent coins. How much money is there in the basket?
|
Fifty-cent (1) |
Ten-cent (2) |
Make u the same (2)x4 = (3) |
Before |
4 u |
1 u |
4 u |
Change |
- 13 |
+ 65 |
+ 260 |
After |
5 p |
11 p |
44 p |
100 + 300100=
400100 =
41 At first
Fifty-cent coins : Ten-cent coins
4 : 1
1 -
611 =
511 In the end
Fifty-cent coins : Ten-cent coins
5 : 11
Total value of 50-cent coins to be taken out
= 13 x 50
= 650¢
Total number of 10-cent coins to be exchanged for
= 650 ÷ 10
= 65
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.
4 u - 13 = 5 p
4 u = 5 p + 13 --- (1)
1 u + 65 = 11 p --- (2)
(2)x4
4 u + 260 = 44 p
4 u = 44 p - 260 --- (3)
(3) = (1)
44 p - 260 = 5 p + 13
44 p - 5 p = 13 + 260
39 p = 273
1 p = 273 ÷ 39 = 7
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 7 x 50
= 1750¢
Total value of ten-cent coins in the end
= 11 p x 10
= 11 x 7 x 10
= 770¢
Total value of the coins
= 1750 + 770
= 2520¢
= $25.20
Answer(s): $25.20