The number of twenty-cent coins in a basket was 300% more than the number of ten-cent coins. 18 twenty-cent coins were taken out and exchanged for ten-cent coins. The number of 20-cent coins became
38 less than the number of 10-cent coins. How much money is there in the basket?
|
Twenty-cent (1) |
Ten-cent (2) |
Make u the same (2)x4 = (3) |
Before |
4 u |
1 u |
4 u |
Change |
- 18 |
+ 36 |
+ 144 |
After |
5 p |
8 p |
32 p |
100 + 300100=
400100 =
41 At first
Twenty-cent coins : Ten-cent coins
4 : 1
1 -
38 =
58 In the end
Twenty-cent coins : Ten-cent coins
5 : 8
Total value of 20-cent coins to be taken out
= 18 x 20
= 360¢
Total number of 10-cent coins to be exchanged for
= 360 ÷ 10
= 36
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 - 18 = 5 p
4 u = 5 p + 18 --- (1)
1 u + 36 = 8 p --- (2)
(2)x4
4 u + 144 = 32 p
4 u = 32 p - 144 --- (3)
(3) = (1)
32 p - 144 = 5 p + 18
32 p - 5 p = 18 + 144
27 p = 162
1 p = 162 ÷ 27 = 6
The total value of the coins at first and in the end remains unchanged.
Total value of twenty-cent coins in the end
= 5 p x 20
= 5 x 6 x 20
= 600¢
Total value of ten-cent coins in the end
= 8 p x 10
= 8 x 6 x 10
= 480¢
Total value of the coins
= 600 + 480
= 1080¢
= $10.80
Answer(s): $10.80