The number of twenty-cent coins in a basket was 200% 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
611 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 |
- 20 |
+ 40 |
+ 120 |
After |
5 p |
11 p |
33 p |
100 + 200100=
300100 =
31 At first
Twenty-cent coins : Ten-cent coins
3 : 1
1 -
611 =
511 In the end
Twenty-cent coins : Ten-cent coins
5 : 11
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.
3 u - 20 = 5 p
3 u = 5 p + 20 --- (1)
1 u + 40 = 11 p --- (2)
(2)x3
3 u + 120 = 33 p
3 u = 33 p - 120 --- (3)
(3) = (1)
33 p - 120 = 5 p + 20
33 p - 5 p = 20 + 120
28 p = 140
1 p = 140 ÷ 28 = 5
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 5 x 20
= 500¢
Total value of ten-cent coins in the end
= 11 p x 10
= 11 x 5 x 10
= 550¢
Total value of the coins
= 500 + 550
= 1050¢
= $10.50
Answer(s): $10.50