The number of twenty-cent coins in a basket was 300% more than the number of ten-cent coins. 17 twenty-cent coins were taken out and exchanged for ten-cent coins. The number of 20-cent coins became
316 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 |
- 17 |
+ 34 |
+ 136 |
After |
13 p |
16 p |
64 p |
100 + 300100=
400100 =
41 At first
Twenty-cent coins : Ten-cent coins
4 : 1
1 -
316 =
1316 In the end
Twenty-cent coins : Ten-cent coins
13 : 16
Total value of 20-cent coins to be taken out
= 17 x 20
= 340¢
Total number of 10-cent coins to be exchanged for
= 340 ÷ 10
= 34
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 - 17 = 13 p
4 u = 13 p + 17 --- (1)
1 u + 34 = 16 p --- (2)
(2)x4
4 u + 136 = 64 p
4 u = 64 p - 136 --- (3)
(3) = (1)
64 p - 136 = 13 p + 17
64 p - 13 p = 17 + 136
51 p = 153
1 p = 153 ÷ 51 = 3
The total value of the coins at first and in the end remains unchanged.
Total value of twenty-cent coins in the end
= 13 p x 20
= 13 x 3 x 20
= 780¢
Total value of ten-cent coins in the end
= 16 p x 10
= 16 x 3 x 10
= 480¢
Total value of the coins
= 780 + 480
= 1260¢
= $12.60
Answer(s): $12.60