The number of twenty-cent coins in a bag was 100% more than the number of ten-cent coins. 9 twenty-cent coins were taken out and exchanged for ten-cent coins. The number of 20-cent coins became
411 less than the number of 10-cent coins. How much money is there in the bag?
|
Twenty-cent (1) |
Ten-cent (2) |
Make u the same (2)x2 = (3) |
Before |
2 u |
1 u |
2 u |
Change |
- 9 |
+ 18 |
+ 36 |
After |
7 p |
11 p |
22 p |
100 + 100100=
200100 =
21 At first
Twenty-cent coins : Ten-cent coins
2 : 1
1 -
411 =
711 In the end
Twenty-cent coins : Ten-cent coins
7 : 11
Total value of 20-cent coins to be taken out
= 9 x 20
= 180¢
Total number of 10-cent coins to be exchanged for
= 180 ÷ 10
= 18
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.
2 u - 9 = 7 p
2 u = 7 p + 9 --- (1)
1 u + 18 = 11 p --- (2)
(2)x2
2 u + 36 = 22 p
2 u = 22 p - 36 --- (3)
(3) = (1)
22 p - 36 = 7 p + 9
22 p - 7 p = 9 + 36
15 p = 45
1 p = 45 ÷ 15 = 3
The total value of the coins at first and in the end remains unchanged.
Total value of twenty-cent coins in the end
= 7 p x 20
= 7 x 3 x 20
= 420¢
Total value of ten-cent coins in the end
= 11 p x 10
= 11 x 3 x 10
= 330¢
Total value of the coins
= 420 + 330
= 750¢
= $7.50
Answer(s): $7.50