The number of fifty-cent coins in a basket was 100% more than the number of twenty-cent coins. 10 fifty-cent coins were taken out and exchanged for twenty-cent coins. The number of 50-cent coins became
411 less than the number of 20-cent coins. How much money is there in the basket?
|
Fifty-cent (1) |
Twenty-cent (2) |
Make u the same (2)x2 = (3) |
Before |
2 u |
1 u |
2 u |
Change |
- 10 |
+ 25 |
+ 50 |
After |
7 p |
11 p |
22 p |
100 + 100100=
200100 =
21 At first
Fifty-cent coins : Twenty-cent coins
2 : 1
1 -
411 =
711 In the end
Fifty-cent coins : Twenty-cent coins
7 : 11
Total value of 50-cent coins to be taken out
= 10 x 50
= 500¢
Total number of 20-cent coins to be exchanged for
= 500 ÷ 20
= 25
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.
2 u - 10 = 7 p
2 u = 7 p + 10 --- (1)
1 u + 25 = 11 p --- (2)
(2)x2
2 u + 50 = 22 p
2 u = 22 p - 50 --- (3)
(3) = (1)
22 p - 50 = 7 p + 10
22 p - 7 p = 10 + 50
15 p = 60
1 p = 60 ÷ 15 = 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 twenty-cent coins in the end
= 11 p x 20
= 11 x 4 x 20
= 880¢
Total value of the coins
= 1400 + 880
= 2280¢
= $22.80
Answer(s): $22.80