The number of fifty-cent coins in a box was 100% more than the number of twenty-cent coins. 18 fifty-cent coins were taken out and exchanged for twenty-cent coins. The number of 50-cent coins became
1116 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)x2 = (3) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 18 |
+ 45 |
+ 90 |
| After |
5 p |
16 p |
32 p |
100 + 100100=
200100 =
21 At first
Fifty-cent coins : Twenty-cent coins
2 : 1
1 -
1116 =
516 In the end
Fifty-cent coins : Twenty-cent coins
5 : 16
Total value of 50-cent coins to be taken out
= 18 x 50
= 900¢
Total number of 20-cent coins to be exchanged for
= 900 ÷ 20
= 45
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 - 18 = 5 p
2 u = 5 p + 18 --- (1)
1 u + 45 = 16 p --- (2)
(2)x2
2 u + 90 = 32 p
2 u = 32 p - 90 --- (3)
(3) = (1)
32 p - 90 = 5 p + 18
32 p - 5 p = 18 + 90
27 p = 108
1 p = 108 ÷ 27 = 4
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 5 p x 50
= 5 x 4 x 50
= 1000¢
Total value of twenty-cent coins in the end
= 16 p x 20
= 16 x 4 x 20
= 1280¢
Total value of the coins
= 1000 + 1280
= 2280¢
= $22.80
Answer(s): $22.80
