The number of fifty-cent coins in a box was 300% more than the number of ten-cent coins. 19 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
916 less than the number of 10-cent coins. How much money is there in the box?
| |
Fifty-cent
(1) |
Ten-cent
(2) |
Make u the same
(2)x4 = (3) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 19 |
+ 95 |
+ 380 |
| After |
7 p |
16 p |
64 p |
100 + 300100=
400100 =
41 At first
Fifty-cent coins : Ten-cent coins
4 : 1
1 -
916 =
716 In the end
Fifty-cent coins : Ten-cent coins
7 : 16
Total value of 50-cent coins to be taken out
= 19 x 50
= 950¢
Total number of 10-cent coins to be exchanged for
= 950 ÷ 10
= 95
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.
4 u - 19 = 7 p
4 u = 7 p + 19 --- (1)
1 u + 95 = 16 p --- (2)
(2)x4
4 u + 380 = 64 p
4 u = 64 p - 380 --- (3)
(3) = (1)
64 p - 380 = 7 p + 19
64 p - 7 p = 19 + 380
57 p = 399
1 p = 399 ÷ 57 = 7
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 7 x 50
= 2450¢
Total value of ten-cent coins in the end
= 16 p x 10
= 16 x 7 x 10
= 1120¢
Total value of the coins
= 2450 + 1120
= 3570¢
= $35.70
Answer(s): $35.70
