The number of fifty-cent coins in a box was 200% 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
49 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 |
- 11 |
+ 55 |
+ 165 |
After |
5 p |
9 p |
27 p |
100 + 200100=
300100 =
31 At first
Fifty-cent coins : Ten-cent coins
3 : 1
1 -
49 =
59 In the end
Fifty-cent coins : Ten-cent coins
5 : 9
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.
3 u - 11 = 5 p
3 u = 5 p + 11 --- (1)
1 u + 55 = 9 p --- (2)
(2)x3
3 u + 165 = 27 p
3 u = 27 p - 165 --- (3)
(3) = (1)
27 p - 165 = 5 p + 11
27 p - 5 p = 11 + 165
22 p = 176
1 p = 176 ÷ 22 = 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
= 9 p x 10
= 9 x 8 x 10
= 720¢
Total value of the coins
= 2000 + 720
= 2720¢
= $27.20
Answer(s): $27.20