A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 6.
When 10 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 |
6 u |
60 u |
Change |
+ 350 |
+ 50 |
- 10 |
- 100 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 10 fifty-cent coins
= 10 x 50
= 500¢
Number of ten-cent coins to exchange for
= 500 ÷ 10
= 50
5 u + 50 = 10 p --- (1)
6 u - 10 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 350 = 70 p --- (3)
(2)
x 10 60 u - 100 = 70 p --- (4)
(4) = (3)
60 u - 100 = 35 u + 350
60 u - 35 u = 350 + 100
25 u = 450
1 u = 450 ÷ 25 = 18
Value of ten-cent coins
= 5 u x 10
= 5 x 18 x 10
= 900¢
Value of fifty-cent coins
= 6 u x 50
= 6 x 18 x 50
= 5400¢
Total value of coins
= 900 + 5400
= 6300¢
100¢ = $1
Sum of money in the coin box
= 6300¢
= $63
Answer(s): $63