The number of twenty-cent coins in a basket was 200% more than the number of ten-cent coins. 19 twenty-cent coins were taken out and exchanged for ten-cent coins. The number of 20-cent coins became
57 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)x3 = (3) |
Before |
3 u |
1 u |
3 u |
Change |
- 19 |
+ 38 |
+ 114 |
After |
2 p |
7 p |
21 p |
100 + 200100=
300100 =
31 At first
Twenty-cent coins : Ten-cent coins
3 : 1
1 -
57 =
27 In the end
Twenty-cent coins : Ten-cent coins
2 : 7
Total value of 20-cent coins to be taken out
= 19 x 20
= 380¢
Total number of 10-cent coins to be exchanged for
= 380 ÷ 10
= 38
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.
3 u - 19 = 2 p
3 u = 2 p + 19 --- (1)
1 u + 38 = 7 p --- (2)
(2)x3
3 u + 114 = 21 p
3 u = 21 p - 114 --- (3)
(3) = (1)
21 p - 114 = 2 p + 19
21 p - 2 p = 19 + 114
19 p = 133
1 p = 133 ÷ 19 = 7
The total value of the coins at first and in the end remains unchanged.
Total value of twenty-cent coins in the end
= 2 p x 20
= 2 x 7 x 20
= 280¢
Total value of ten-cent coins in the end
= 7 p x 10
= 7 x 7 x 10
= 490¢
Total value of the coins
= 280 + 490
= 770¢
= $7.70
Answer(s): $7.70