A coin bank contains some ten-cent and twenty-cent coins in the ratio of 5 : 6.
When 20 twenty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 7 : 8.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 8 = (3) |
(1) 10-cent |
(2) 20-cent |
Make p the same. (2) x 7 = (4) |
Before |
40 u |
5 u |
6 u |
42 u |
Change |
+ 320 |
+ 40 |
- 20 |
- 140 |
After |
56 p |
7 p |
8 p |
56 p |
Value of 20 twenty-cent coins
= 20 x 20
= 400¢
Number of ten-cent coins to exchange for
= 400 ÷ 10
= 40
5 u + 40 = 7 p --- (1)
6 u - 20 = 8 p --- (2)
Make p the same.
(1)
x 8 40 u + 320 = 56 p --- (3)
(2)
x 7 42 u - 140 = 56 p --- (4)
(4) = (3)
42 u - 140 = 40 u + 320
42 u - 40 u = 320 + 140
2 u = 460
1 u = 460 ÷ 2 = 230
Value of ten-cent coins
= 5 u x 10
= 5 x 230 x 10
= 11500¢
Value of twenty-cent coins
= 6 u x 20
= 6 x 230 x 20
= 27600¢
Total value of coins
= 11500 + 27600
= 39100¢
100¢ = $1
Sum of money in the coin box
= 39100¢
= $391
Answer(s): $391