The number of fifty-cent coins in a bag was 300% more than the number of ten-cent coins. 11 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
310 less than the number of 10-cent coins. How much money is there in the bag?
|
Fifty-cent (1) |
Ten-cent (2) |
Make u the same (2)x4 = (3) |
Before |
4 u |
1 u |
4 u |
Change |
- 11 |
+ 55 |
+ 220 |
After |
7 p |
10 p |
40 p |
100 + 300100=
400100 =
41 At first
Fifty-cent coins : Ten-cent coins
4 : 1
1 -
310 =
710 In the end
Fifty-cent coins : Ten-cent coins
7 : 10
Total value of 50-cent coins to be taken out
= 11 x 50
= 550¢
Total number of 10-cent coins to be exchanged for
= 550 ÷ 10
= 55
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.
4 u - 11 = 7 p
4 u = 7 p + 11 --- (1)
1 u + 55 = 10 p --- (2)
(2)x4
4 u + 220 = 40 p
4 u = 40 p - 220 --- (3)
(3) = (1)
40 p - 220 = 7 p + 11
40 p - 7 p = 11 + 220
33 p = 231
1 p = 231 ÷ 33 = 7
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 7 x 50
= 2450¢
Total value of ten-cent coins in the end
= 10 p x 10
= 10 x 7 x 10
= 700¢
Total value of the coins
= 2450 + 700
= 3150¢
= $31.50
Answer(s): $31.50