The number of fifty-cent coins in a bag was 300% more than the number of ten-cent coins. 15 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 bag?
|
Fifty-cent (1) |
Ten-cent (2) |
Make u the same (2)x4 = (3) |
Before |
4 u |
1 u |
4 u |
Change |
- 15 |
+ 75 |
+ 300 |
After |
7 p |
13 p |
52 p |
100 + 300100=
400100 =
41 At first
Fifty-cent coins : Ten-cent coins
4 : 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
= 15 x 50
= 750¢
Total number of 10-cent coins to be exchanged for
= 750 ÷ 10
= 75
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 - 15 = 7 p
4 u = 7 p + 15 --- (1)
1 u + 75 = 13 p --- (2)
(2)x4
4 u + 300 = 52 p
4 u = 52 p - 300 --- (3)
(3) = (1)
52 p - 300 = 7 p + 15
52 p - 7 p = 15 + 300
45 p = 315
1 p = 315 ÷ 45 = 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
= 13 p x 10
= 13 x 7 x 10
= 910¢
Total value of the coins
= 2450 + 910
= 3360¢
= $33.60
Answer(s): $33.60