The number of twenty-cent coins in a basket was 300% more than the number of ten-cent coins. 20 twenty-cent coins were taken out and exchanged for ten-cent coins. The number of 20-cent coins became
613 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 |
- 20 |
+ 40 |
+ 160 |
After |
7 p |
13 p |
52 p |
100 + 300100=
400100 =
41 At first
Twenty-cent coins : Ten-cent coins
4 : 1
1 -
613 =
713 In the end
Twenty-cent coins : Ten-cent coins
7 : 13
Total value of 20-cent coins to be taken out
= 20 x 20
= 400¢
Total number of 10-cent coins to be exchanged for
= 400 ÷ 10
= 40
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 - 20 = 7 p
4 u = 7 p + 20 --- (1)
1 u + 40 = 13 p --- (2)
(2)x4
4 u + 160 = 52 p
4 u = 52 p - 160 --- (3)
(3) = (1)
52 p - 160 = 7 p + 20
52 p - 7 p = 20 + 160
45 p = 180
1 p = 180 ÷ 45 = 4
The total value of the coins at first and in the end remains unchanged.
Total value of twenty-cent coins in the end
= 7 p x 20
= 7 x 4 x 20
= 560¢
Total value of ten-cent coins in the end
= 13 p x 10
= 13 x 4 x 10
= 520¢
Total value of the coins
= 560 + 520
= 1080¢
= $10.80
Answer(s): $10.80