A coin bank contains some five-cent and fifty-cent coins in the ratio of 3 : 4.
When 19 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 |
21 u |
3 u |
4 u |
40 u |
Change |
+ 1330 |
+ 190 |
- 19 |
- 190 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 19 fifty-cent coins
= 19 x 50
= 950¢
Number of five-cent coins to exchange for
= 950 ÷ 5
= 190
3 u + 190 = 10 p --- (1)
4 u - 19 = 7 p --- (2)
Make p the same.
(1)
x 7 21 u + 1330 = 70 p --- (3)
(2)
x 10 40 u - 190 = 70 p --- (4)
(4) = (3)
40 u - 190 = 21 u + 1330
40 u - 21 u = 1330 + 190
19 u = 1520
1 u = 1520 ÷ 19 = 80
Value of five-cent coins
= 3 u x 5
= 3 x 80 x 5
= 1200¢
Value of fifty-cent coins
= 4 u x 50
= 4 x 80 x 50
= 16000¢
Total value of coins
= 1200 + 16000
= 17200¢
100¢ = $1
Sum of money in the coin box
= 17200¢
= $172
Answer(s): $172