The number of fifty-cent coins in a basket was 200% more than the number of ten-cent coins. 12 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
613 less than the number of 10-cent coins. How much money is there in the basket?
|
Fifty-cent (1) |
Ten-cent (2) |
Make u the same (2)x3 = (3) |
Before |
3 u |
1 u |
3 u |
Change |
- 12 |
+ 60 |
+ 180 |
After |
7 p |
13 p |
39 p |
100 + 200100=
300100 =
31 At first
Fifty-cent coins : Ten-cent coins
3 : 1
1 -
613 =
713 In the end
Fifty-cent coins : Ten-cent coins
7 : 13
Total value of 50-cent coins to be taken out
= 12 x 50
= 600¢
Total number of 10-cent coins to be exchanged for
= 600 ÷ 10
= 60
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 = 7 p
3 u = 7 p + 12 --- (1)
1 u + 60 = 13 p --- (2)
(2)x3
3 u + 180 = 39 p
3 u = 39 p - 180 --- (3)
(3) = (1)
39 p - 180 = 7 p + 12
39 p - 7 p = 12 + 180
32 p = 192
1 p = 192 ÷ 32 = 6
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 7 p x 50
= 7 x 6 x 50
= 2100¢
Total value of ten-cent coins in the end
= 13 p x 10
= 13 x 6 x 10
= 780¢
Total value of the coins
= 2100 + 780
= 2880¢
= $28.80
Answer(s): $28.80