The number of fifty-cent coins in a box was 200% more than the number of twenty-cent coins. 12 fifty-cent coins were taken out and exchanged for twenty-cent coins. The number of 50-cent coins became
415 less than the number of 20-cent coins. How much money is there in the box?
|
Fifty-cent (1) |
Twenty-cent (2) |
Make u the same (2)x3 = (3) |
Before |
3 u |
1 u |
3 u |
Change |
- 12 |
+ 30 |
+ 90 |
After |
11 p |
15 p |
45 p |
100 + 200100=
300100 =
31 At first
Fifty-cent coins : Twenty-cent coins
3 : 1
1 -
415 =
1115 In the end
Fifty-cent coins : Twenty-cent coins
11 : 15
Total value of 50-cent coins to be taken out
= 12 x 50
= 600¢
Total number of 20-cent coins to be exchanged for
= 600 ÷ 20
= 30
Notice that the number of 20-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 - 12 = 11 p
3 u = 11 p + 12 --- (1)
1 u + 30 = 15 p --- (2)
(2)x3
3 u + 90 = 45 p
3 u = 45 p - 90 --- (3)
(3) = (1)
45 p - 90 = 11 p + 12
45 p - 11 p = 12 + 90
34 p = 102
1 p = 102 ÷ 34 = 3
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 11 p x 50
= 11 x 3 x 50
= 1650¢
Total value of twenty-cent coins in the end
= 15 p x 20
= 15 x 3 x 20
= 900¢
Total value of the coins
= 1650 + 900
= 2550¢
= $25.50
Answer(s): $25.50