The number of fifty-cent coins in a box was 200% more than the number of ten-cent coins. 5 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
29 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 |
- 5 |
+ 25 |
+ 75 |
After |
7 p |
9 p |
27 p |
100 + 200100=
300100 =
31 At first
Fifty-cent coins : Ten-cent coins
3 : 1
1 -
29 =
79 In the end
Fifty-cent coins : Ten-cent coins
7 : 9
Total value of 50-cent coins to be taken out
= 5 x 50
= 250¢
Total number of 10-cent coins to be exchanged for
= 250 ÷ 10
= 25
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 - 5 = 7 p
3 u = 7 p + 5 --- (1)
1 u + 25 = 9 p --- (2)
(2)x3
3 u + 75 = 27 p
3 u = 27 p - 75 --- (3)
(3) = (1)
27 p - 75 = 7 p + 5
27 p - 7 p = 5 + 75
20 p = 80
1 p = 80 ÷ 20 = 4
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 4 x 50
= 1400¢
Total value of ten-cent coins in the end
= 9 p x 10
= 9 x 4 x 10
= 360¢
Total value of the coins
= 1400 + 360
= 1760¢
= $17.60
Answer(s): $17.60