The number of fifty-cent coins in a box was 200% more than the number of ten-cent coins. 9 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
27 less than the number of 10-cent coins. How much money is there in the box?
|
Fifty-cent (1) |
Ten-cent (2) |
Make u the same (2)x3 = (3) |
Before |
3 u |
1 u |
3 u |
Change |
- 9 |
+ 45 |
+ 135 |
After |
5 p |
7 p |
21 p |
100 + 200100=
300100 =
31 At first
Fifty-cent coins : Ten-cent coins
3 : 1
1 -
27 =
57 In the end
Fifty-cent coins : Ten-cent coins
5 : 7
Total value of 50-cent coins to be taken out
= 9 x 50
= 450¢
Total number of 10-cent coins to be exchanged for
= 450 ÷ 10
= 45
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 - 9 = 5 p
3 u = 5 p + 9 --- (1)
1 u + 45 = 7 p --- (2)
(2)x3
3 u + 135 = 21 p
3 u = 21 p - 135 --- (3)
(3) = (1)
21 p - 135 = 5 p + 9
21 p - 5 p = 9 + 135
16 p = 144
1 p = 144 ÷ 16 = 9
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 9 x 50
= 2250¢
Total value of ten-cent coins in the end
= 7 p x 10
= 7 x 9 x 10
= 630¢
Total value of the coins
= 2250 + 630
= 2880¢
= $28.80
Answer(s): $28.80