The number of twenty-cent coins in a basket was 200% more than the number of ten-cent coins. 12 twenty-cent coins were taken out and exchanged for ten-cent coins. The number of 20-cent coins became
213 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 |
- 12 |
+ 24 |
+ 72 |
After |
11 p |
13 p |
39 p |
100 + 200100=
300100 =
31 At first
Twenty-cent coins : Ten-cent coins
3 : 1
1 -
213 =
1113 In the end
Twenty-cent coins : Ten-cent coins
11 : 13
Total value of 20-cent coins to be taken out
= 12 x 20
= 240¢
Total number of 10-cent coins to be exchanged for
= 240 ÷ 10
= 24
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 - 12 = 11 p
3 u = 11 p + 12 --- (1)
1 u + 24 = 13 p --- (2)
(2)x3
3 u + 72 = 39 p
3 u = 39 p - 72 --- (3)
(3) = (1)
39 p - 72 = 11 p + 12
39 p - 11 p = 12 + 72
28 p = 84
1 p = 84 ÷ 28 = 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
= 13 p x 10
= 13 x 3 x 10
= 390¢
Total value of the coins
= 660 + 390
= 1050¢
= $10.50
Answer(s): $10.50