A coin bank contains some five-cent and fifty-cent coins in the ratio of 2 : 7.
When 14 fifty-cent coins are taken out and
exchanged with some five-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) 5-cent |
(2) 50-cent |
Make p the same. (2) x 10 = (4) |
Before |
14 u |
2 u |
7 u |
70 u |
Change |
+ 980 |
+ 140 |
- 14 |
- 140 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 14 fifty-cent coins
= 14 x 50
= 700¢
Number of five-cent coins to exchange for
= 700 ÷ 5
= 140
2 u + 140 = 10 p --- (1)
7 u - 14 = 7 p --- (2)
Make p the same.
(1)
x 7 14 u + 980 = 70 p --- (3)
(2)
x 10 70 u - 140 = 70 p --- (4)
(4) = (3)
70 u - 140 = 14 u + 980
70 u - 14 u = 980 + 140
56 u = 1120
1 u = 1120 ÷ 56 = 20
Value of five-cent coins
= 2 u x 5
= 2 x 20 x 5
= 200¢
Value of fifty-cent coins
= 7 u x 50
= 7 x 20 x 50
= 7000¢
Total value of coins
= 200 + 7000
= 7200¢
100¢ = $1
Sum of money in the coin box
= 7200¢
= $72
Answer(s): $72