The number of twenty-cent coins in a basket was 200% more than the number of ten-cent coins. 15 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 basket?
|
Twenty-cent (1) |
Ten-cent (2) |
Make u the same (2)x3 = (3) |
Before |
3 u |
1 u |
3 u |
Change |
- 15 |
+ 30 |
+ 90 |
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
= 15 x 20
= 300¢
Total number of 10-cent coins to be exchanged for
= 300 ÷ 10
= 30
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 - 15 = 13 p
3 u = 13 p + 15 --- (1)
1 u + 30 = 16 p --- (2)
(2)x3
3 u + 90 = 48 p
3 u = 48 p - 90 --- (3)
(3) = (1)
48 p - 90 = 13 p + 15
48 p - 13 p = 15 + 90
35 p = 105
1 p = 105 ÷ 35 = 3
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 3 x 20
= 780¢
Total value of ten-cent coins in the end
= 16 p x 10
= 16 x 3 x 10
= 480¢
Total value of the coins
= 780 + 480
= 1260¢
= $12.60
Answer(s): $12.60