The number of twenty-cent coins in a box was 200% more than the number of ten-cent coins. 10 twenty-cent coins were taken out and exchanged for ten-cent coins. The number of 20-cent coins became
316 less than the number of 10-cent coins. How much money is there in the box?
| |
Twenty-cent
(1) |
Ten-cent
(2) |
Make u the same
(2)x3 = (3) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 10 |
+ 20 |
+ 60 |
| After |
13 p |
16 p |
48 p |
100 + 200100=
300100 =
31 At first
Twenty-cent coins : Ten-cent coins
3 : 1
1 -
316 =
1316 In the end
Twenty-cent coins : Ten-cent coins
13 : 16
Total value of 20-cent coins to be taken out
= 10 x 20
= 200¢
Total number of 10-cent coins to be exchanged for
= 200 ÷ 10
= 20
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 - 10 = 13 p
3 u = 13 p + 10 --- (1)
1 u + 20 = 16 p --- (2)
(2)x3
3 u + 60 = 48 p
3 u = 48 p - 60 --- (3)
(3) = (1)
48 p - 60 = 13 p + 10
48 p - 13 p = 10 + 60
35 p = 70
1 p = 70 ÷ 35 = 2
The total value of the coins at first and in the end remains unchanged.
Total value of twenty-cent coins in the end
= 13 p x 20
= 13 x 2 x 20
= 520¢
Total value of ten-cent coins in the end
= 16 p x 10
= 16 x 2 x 10
= 320¢
Total value of the coins
= 520 + 320
= 840¢
= $8.40
Answer(s): $8.40
