A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 4.
When 14 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 8 : 5.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 5 = (3) |
(1) 10-cent |
(2) 50-cent |
Make p the same. (2) x 8 = (4) |
Before |
25 u |
5 u |
4 u |
32 u |
Change |
+ 350 |
+ 70 |
- 14 |
- 112 |
After |
40 p |
8 p |
5 p |
40 p |
Value of 14 fifty-cent coins
= 14 x 50
= 700¢
Number of ten-cent coins to exchange for
= 700 ÷ 10
= 70
5 u + 70 = 8 p --- (1)
4 u - 14 = 5 p --- (2)
Make p the same.
(1)
x 5 25 u + 350 = 40 p --- (3)
(2)
x 8 32 u - 112 = 40 p --- (4)
(4) = (3)
32 u - 112 = 25 u + 350
32 u - 25 u = 350 + 112
7 u = 462
1 u = 462 ÷ 7 = 66
Value of ten-cent coins
= 5 u x 10
= 5 x 66 x 10
= 3300¢
Value of fifty-cent coins
= 4 u x 50
= 4 x 66 x 50
= 13200¢
Total value of coins
= 3300 + 13200
= 16500¢
100¢ = $1
Sum of money in the coin box
= 16500¢
= $165
Answer(s): $165