The number of fifty-cent coins in a basket was 200% more than the number of ten-cent coins. 17 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
813 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 |
- 17 |
+ 85 |
+ 255 |
After |
5 p |
13 p |
39 p |
100 + 200100=
300100 =
31 At first
Fifty-cent coins : Ten-cent coins
3 : 1
1 -
813 =
513 In the end
Fifty-cent coins : Ten-cent coins
5 : 13
Total value of 50-cent coins to be taken out
= 17 x 50
= 850¢
Total number of 10-cent coins to be exchanged for
= 850 ÷ 10
= 85
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 - 17 = 5 p
3 u = 5 p + 17 --- (1)
1 u + 85 = 13 p --- (2)
(2)x3
3 u + 255 = 39 p
3 u = 39 p - 255 --- (3)
(3) = (1)
39 p - 255 = 5 p + 17
39 p - 5 p = 17 + 255
34 p = 272
1 p = 272 ÷ 34 = 8
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 5 p x 50
= 5 x 8 x 50
= 2000¢
Total value of ten-cent coins in the end
= 13 p x 10
= 13 x 8 x 10
= 1040¢
Total value of the coins
= 2000 + 1040
= 3040¢
= $30.40
Answer(s): $30.40