A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5.
When 16 fifty-cent coins are taken out and
exchanged with some twenty-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) 20-cent |
(2) 50-cent |
Make p the same. (2) x 10 = (4) |
Before |
28 u |
4 u |
5 u |
50 u |
Change |
+ 280 |
+ 40 |
- 16 |
- 160 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 16 fifty-cent coins
= 16 x 50
= 800¢
Number of twenty-cent coins to exchange for
= 800 ÷ 20
= 40
4 u + 40 = 10 p --- (1)
5 u - 16 = 7 p --- (2)
Make p the same.
(1)
x 7 28 u + 280 = 70 p --- (3)
(2)
x 10 50 u - 160 = 70 p --- (4)
(4) = (3)
50 u - 160 = 28 u + 280
50 u - 28 u = 280 + 160
22 u = 440
1 u = 440 ÷ 22 = 20
Value of twenty-cent coins
= 4 u x 20
= 4 x 20 x 20
= 1600¢
Value of fifty-cent coins
= 5 u x 50
= 5 x 20 x 50
= 5000¢
Total value of coins
= 1600 + 5000
= 6600¢
100¢ = $1
Sum of money in the coin box
= 6600¢
= $66
Answer(s): $66