The number of twenty-cent coins in a basket was 300% more than the number of ten-cent coins. 15 twenty-cent coins were taken out and exchanged for ten-cent coins. The number of 20-cent coins became
314 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 |
- 15 |
+ 30 |
+ 120 |
| After |
11 p |
14 p |
56 p |
100 + 300100=
400100 =
41 At first
Twenty-cent coins : Ten-cent coins
4 : 1
1 -
314 =
1114 In the end
Twenty-cent coins : Ten-cent coins
11 : 14
Total value of 20-cent coins to be taken out
= 15 x 20
= 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.
4 u - 15 = 11 p
4 u = 11 p + 15 --- (1)
1 u + 30 = 14 p --- (2)
(2)x4
4 u + 120 = 56 p
4 u = 56 p - 120 --- (3)
(3) = (1)
56 p - 120 = 11 p + 15
56 p - 11 p = 15 + 120
45 p = 135
1 p = 135 ÷ 45 = 3
The total value of the coins at first and in the end remains unchanged.
Total value of twenty-cent coins in the end
= 11 p x 20
= 11 x 3 x 20
= 660¢
Total value of ten-cent coins in the end
= 14 p x 10
= 14 x 3 x 10
= 420¢
Total value of the coins
= 660 + 420
= 1080¢
= $10.80
Answer(s): $10.80
