A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 4.
When 6 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 10 : 7.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 7 = (3) |
(1) 10-cent |
(2) 50-cent |
Make p the same. (2) x 10 = (4) |
Before |
35 u |
5 u |
4 u |
40 u |
Change |
+ 210 |
+ 30 |
- 6 |
- 60 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 6 fifty-cent coins
= 6 x 50
= 300¢
Number of ten-cent coins to exchange for
= 300 ÷ 10
= 30
5 u + 30 = 10 p --- (1)
4 u - 6 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 210 = 70 p --- (3)
(2)
x 10 40 u - 60 = 70 p --- (4)
(4) = (3)
40 u - 60 = 35 u + 210
40 u - 35 u = 210 + 60
5 u = 270
1 u = 270 ÷ 5 = 54
Value of ten-cent coins
= 5 u x 10
= 5 x 54 x 10
= 2700¢
Value of fifty-cent coins
= 4 u x 50
= 4 x 54 x 50
= 10800¢
Total value of coins
= 2700 + 10800
= 13500¢
100¢ = $1
Sum of money in the coin box
= 13500¢
= $135
Answer(s): $135