A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 7.
When 7 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 9 : 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 9 = (4) |
Before |
35 u |
5 u |
7 u |
63 u |
Change |
+ 245 |
+ 35 |
- 7 |
- 63 |
After |
63 p |
9 p |
7 p |
63 p |
Value of 7 fifty-cent coins
= 7 x 50
= 350¢
Number of ten-cent coins to exchange for
= 350 ÷ 10
= 35
5 u + 35 = 9 p --- (1)
7 u - 7 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 245 = 63 p --- (3)
(2)
x 9 63 u - 63 = 63 p --- (4)
(4) = (3)
63 u - 63 = 35 u + 245
63 u - 35 u = 245 + 63
28 u = 308
1 u = 308 ÷ 28 = 11
Value of ten-cent coins
= 5 u x 10
= 5 x 11 x 10
= 550¢
Value of fifty-cent coins
= 7 u x 50
= 7 x 11 x 50
= 3850¢
Total value of coins
= 550 + 3850
= 4400¢
100¢ = $1
Sum of money in the coin box
= 4400¢
= $44
Answer(s): $44